Theorem: LRAT.DefaultFormula.derivedLits_nodup (LeanSAT/LRAT/Formula/RupAddResult.lean)

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
⊢ derivedLits_arr[i] ≠ derivedLits_arr[j]
Tactic:
intro li_eq_lj
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
⊢ False
Tactic:
let li := derivedLits_arr[i]
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
⊢ False
Tactic:
have li_in_derivedLits : li ∈ derivedLits := by
  have derivedLits_rw : derivedLits = (Array.mk derivedLits).data := by simp only
  simp only [derivedLits_arr_def, li]
  conv => rhs; rw [derivedLits_rw]
  apply Array.getElem_mem_data
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
⊢ False
Tactic:
have i_in_bounds : i.1 < derivedLits.length := by
  have i_property := i.2
  simp only [derivedLits_arr_def, Array.size_mk] at i_property
  exact i_property
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
⊢ False
Tactic:
have j_in_bounds : j.1 < derivedLits.length := by
  have j_property := j.2
  simp only [derivedLits_arr_def, Array.size_mk] at j_property
  exact j_property
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
⊢ False
Tactic:
rcases derivedLits_satisfies_invariant ⟨li.1.1, li.1.2.2⟩ with ⟨_, h2⟩ | ⟨k, _, _, _, h3⟩ |
  ⟨k1, k2, _, _, k1_eq_true, k2_eq_false, _, _, h3⟩
State after:
case inl.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
left✝ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = f.assignments[↑⟨li.fst.val, ⋯⟩]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inl.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
case inl.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
left✝ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = f.assignments[↑⟨li.fst.val, ⋯⟩]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inl.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
. exact h2 li li_in_derivedLits rfl
State after:
case inr.inl.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
case inr.inl.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
. by_cases k.1 = i.1
  . next k_eq_i =>
    have j_ne_k : ⟨j.1, j_in_bounds⟩ ≠ k := by
      intro j_eq_k
      simp only [← j_eq_k] at k_eq_i
      exact i_ne_j $ Fin.eq_of_val_eq (Eq.symm k_eq_i)
    specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k
    simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
    simp only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li, li_eq_lj] at h3
    simp only [Array.getElem_eq_data_get, not_true] at h3
  . next k_ne_i =>
    have i_ne_k : ⟨i.1, i_in_bounds⟩ ≠ k := by intro i_eq_k; simp only [← i_eq_k, not_true] at k_ne_i
    specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k
    simp (config := { decide := true }) only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, Array.getElem_eq_data_get, li] at h3
State after:
case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
. by_cases li.2 = true
  . next li_eq_true =>
    have i_ne_k2 : ⟨i.1, i_in_bounds⟩ ≠ k2 := by
      intro i_eq_k2
      rw [← i_eq_k2] at k2_eq_false
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li] at li_eq_true
    have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
      intro j_eq_k2
      rw [← j_eq_k2] at k2_eq_false
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li_eq_lj, li] at li_eq_true
    by_cases ⟨i.1, i_in_bounds⟩ = k1
    . next i_eq_k1 =>
      have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
        intro j_eq_k1
        rw [← j_eq_k1] at i_eq_k1
        simp only [Fin.mk.injEq] at i_eq_k1
        exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
      specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
      simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
    . next i_ne_k1 =>
      specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
      simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
  . next li_eq_false =>
    simp only [Bool.not_eq_true] at li_eq_false
    have i_ne_k1 : ⟨i.1, i_in_bounds⟩ ≠ k1 := by
      intro i_eq_k1
      rw [← i_eq_k1] at k1_eq_true
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li] at li_eq_false
    have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
      intro j_eq_k1
      rw [← j_eq_k1] at k1_eq_true
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
      simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li_eq_lj, li] at li_eq_false
    by_cases ⟨i.1, i_in_bounds⟩ = k2
    . next i_eq_k2 =>
      have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
        intro j_eq_k2
        rw [← j_eq_k2] at i_eq_k2
        simp only [Fin.mk.injEq] at i_eq_k2
        exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
      specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
      simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
    . next i_ne_k2 =>
      specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
      simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
⊢ li ∈ derivedLits
Tactic:
have derivedLits_rw : derivedLits = (Array.mk derivedLits).data := by simp only
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ li ∈ derivedLits

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ li ∈ derivedLits
Tactic:
simp only [derivedLits_arr_def, li]
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ { data := derivedLits }[i] ∈ derivedLits

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ { data := derivedLits }[i] ∈ derivedLits
Tactic:
conv => rhs; rw [derivedLits_rw]
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ { data := derivedLits }[i] ∈ { data := derivedLits }.data

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
derivedLits_rw : derivedLits = { data := derivedLits }.data
⊢ { data := derivedLits }[i] ∈ { data := derivedLits }.data
Tactic:
apply Array.getElem_mem_data
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
⊢ derivedLits = { data := derivedLits }.data
Tactic:
simp only
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
⊢ ↑i < derivedLits.length
Tactic:
have i_property := i.2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_property : ↑i < derivedLits_arr.size
⊢ ↑i < derivedLits.length

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_property : ↑i < derivedLits_arr.size
⊢ ↑i < derivedLits.length
Tactic:
simp only [derivedLits_arr_def, Array.size_mk] at i_property
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_property : ↑i < derivedLits.length
⊢ ↑i < derivedLits.length

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_property : ↑i < derivedLits.length
⊢ ↑i < derivedLits.length
Tactic:
exact i_property
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
⊢ ↑j < derivedLits.length
Tactic:
have j_property := j.2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_property : ↑j < derivedLits_arr.size
⊢ ↑j < derivedLits.length

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_property : ↑j < derivedLits_arr.size
⊢ ↑j < derivedLits.length
Tactic:
simp only [derivedLits_arr_def, Array.size_mk] at j_property
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_property : ↑j < derivedLits.length
⊢ ↑j < derivedLits.length

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_property : ↑j < derivedLits.length
⊢ ↑j < derivedLits.length
Tactic:
exact j_property
State after:
no goals

State before:
case inl.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
left✝ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = f.assignments[↑⟨li.fst.val, ⋯⟩]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
exact h2 li li_in_derivedLits rfl
State after:
no goals

State before:
case inr.inl.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
by_cases k.1 = i.1
State after:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ↑k = ↑i
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬↑k = ↑i
⊢ False

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ↑k = ↑i
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬↑k = ↑i
⊢ False
Tactic:
. next k_eq_i =>
  have j_ne_k : ⟨j.1, j_in_bounds⟩ ≠ k := by
    intro j_eq_k
    simp only [← j_eq_k] at k_eq_i
    exact i_ne_j $ Fin.eq_of_val_eq (Eq.symm k_eq_i)
  specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k
  simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
  simp only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li, li_eq_lj] at h3
  simp only [Array.getElem_eq_data_get, not_true] at h3
State after:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬↑k = ↑i
⊢ False

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬↑k = ↑i
⊢ False
Tactic:
. next k_ne_i =>
  have i_ne_k : ⟨i.1, i_in_bounds⟩ ≠ k := by intro i_eq_k; simp only [← i_eq_k, not_true] at k_ne_i
  specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k
  simp (config := { decide := true }) only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, Array.getElem_eq_data_get, li] at h3
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ↑k = ↑i
⊢ False
Tactic:
next k_eq_i =>
have j_ne_k : ⟨j.1, j_in_bounds⟩ ≠ k := by
  intro j_eq_k
  simp only [← j_eq_k] at k_eq_i
  exact i_ne_j $ Fin.eq_of_val_eq (Eq.symm k_eq_i)
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k
simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
simp only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li, li_eq_lj] at h3
simp only [Array.getElem_eq_data_get, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
⊢ False
Tactic:
have j_ne_k : ⟨j.1, j_in_bounds⟩ ≠ k := by
  intro j_eq_k
  simp only [← j_eq_k] at k_eq_i
  exact i_ne_j $ Fin.eq_of_val_eq (Eq.symm k_eq_i)
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
⊢ False
Tactic:
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_lj : { data := derivedLits }[↑i] = { data := derivedLits }[↑j]
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_lj : { data := derivedLits }[↑i] = { data := derivedLits }[↑j]
⊢ False
Tactic:
simp only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li, li_eq_lj] at h3
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
li_eq_lj : { data := derivedLits }[↑i] = { data := derivedLits }[↑j]
h3 : ¬(derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val = { data := derivedLits }[↑j].fst.val
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_eq_i : ↑k = ↑i
j_ne_k : ⟨↑j, j_in_bounds⟩ ≠ k
li_eq_lj : { data := derivedLits }[↑i] = { data := derivedLits }[↑j]
h3 : ¬(derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val = { data := derivedLits }[↑j].fst.val
⊢ False
Tactic:
simp only [Array.getElem_eq_data_get, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
⊢ ⟨↑j, j_in_bounds⟩ ≠ k
Tactic:
intro j_eq_k
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
j_eq_k : ⟨↑j, j_in_bounds⟩ = k
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_eq_i : ↑k = ↑i
j_eq_k : ⟨↑j, j_in_bounds⟩ = k
⊢ False
Tactic:
simp only [← j_eq_k] at k_eq_i
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
j_eq_k : ⟨↑j, j_in_bounds⟩ = k
k_eq_i : ↑j = ↑i
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
j_eq_k : ⟨↑j, j_in_bounds⟩ = k
k_eq_i : ↑j = ↑i
⊢ False
Tactic:
exact i_ne_j $ Fin.eq_of_val_eq (Eq.symm k_eq_i)
State after:
no goals

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬↑k = ↑i
⊢ False
Tactic:
next k_ne_i =>
have i_ne_k : ⟨i.1, i_in_bounds⟩ ≠ k := by intro i_eq_k; simp only [← i_eq_k, not_true] at k_ne_i
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k
simp (config := { decide := true }) only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, Array.getElem_eq_data_get, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
⊢ False
Tactic:
have i_ne_k : ⟨i.1, i_in_bounds⟩ ≠ k := by intro i_eq_k; simp only [← i_eq_k, not_true] at k_ne_i
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
i_ne_k : ⟨↑i, i_in_bounds⟩ ≠ k
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
i_ne_k : ⟨↑i, i_in_bounds⟩ ≠ k
⊢ False
Tactic:
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_ne_i : ¬↑k = ↑i
i_ne_k : ⟨↑i, i_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑i, i_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
k_ne_i : ¬↑k = ↑i
i_ne_k : ⟨↑i, i_in_bounds⟩ ≠ k
h3 : (derivedLits.get ⟨↑i, i_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
simp (config := { decide := true }) only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, Array.getElem_eq_data_get, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
⊢ ⟨↑i, i_in_bounds⟩ ≠ k
Tactic:
intro i_eq_k
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
i_eq_k : ⟨↑i, i_in_bounds⟩ = k
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k : Fin derivedLits.length
left✝² : (derivedLits.get k).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝¹ :
  (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] =
    addAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩]
left✝ : ¬hasAssignment (derivedLits.get k).snd f.assignments[↑⟨li.fst.val, ⋯⟩] = true
h3 : ∀ (k_1 : Fin derivedLits.length), k_1 ≠ k → (derivedLits.get k_1).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
k_ne_i : ¬↑k = ↑i
i_eq_k : ⟨↑i, i_in_bounds⟩ = k
⊢ False
Tactic:
simp only [← i_eq_k, not_true] at k_ne_i
State after:
no goals

State before:
case inr.inr.intro.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
by_cases li.2 = true
State after:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : li.snd = true
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬li.snd = true
⊢ False

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : li.snd = true
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬li.snd = true
⊢ False
Tactic:
. next li_eq_true =>
  have i_ne_k2 : ⟨i.1, i_in_bounds⟩ ≠ k2 := by
    intro i_eq_k2
    rw [← i_eq_k2] at k2_eq_false
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li] at li_eq_true
  have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
    intro j_eq_k2
    rw [← j_eq_k2] at k2_eq_false
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li_eq_lj, li] at li_eq_true
  by_cases ⟨i.1, i_in_bounds⟩ = k1
  . next i_eq_k1 =>
    have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
      intro j_eq_k1
      rw [← j_eq_k1] at i_eq_k1
      simp only [Fin.mk.injEq] at i_eq_k1
      exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
    specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
    simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
  . next i_ne_k1 =>
    specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
    simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬li.snd = true
⊢ False

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬li.snd = true
⊢ False
Tactic:
. next li_eq_false =>
  simp only [Bool.not_eq_true] at li_eq_false
  have i_ne_k1 : ⟨i.1, i_in_bounds⟩ ≠ k1 := by
    intro i_eq_k1
    rw [← i_eq_k1] at k1_eq_true
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li] at li_eq_false
  have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
    intro j_eq_k1
    rw [← j_eq_k1] at k1_eq_true
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
    simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li_eq_lj, li] at li_eq_false
  by_cases ⟨i.1, i_in_bounds⟩ = k2
  . next i_eq_k2 =>
    have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
      intro j_eq_k2
      rw [← j_eq_k2] at i_eq_k2
      simp only [Fin.mk.injEq] at i_eq_k2
      exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
    specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
    simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
  . next i_ne_k2 =>
    specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
    simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : li.snd = true
⊢ False
Tactic:
next li_eq_true =>
have i_ne_k2 : ⟨i.1, i_in_bounds⟩ ≠ k2 := by
  intro i_eq_k2
  rw [← i_eq_k2] at k2_eq_false
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li] at li_eq_true
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
  intro j_eq_k2
  rw [← j_eq_k2] at k2_eq_false
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li_eq_lj, li] at li_eq_true
by_cases ⟨i.1, i_in_bounds⟩ = k1
. next i_eq_k1 =>
  have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
    intro j_eq_k1
    rw [← j_eq_k1] at i_eq_k1
    simp only [Fin.mk.injEq] at i_eq_k1
    exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
  specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
  simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
. next i_ne_k1 =>
  specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
  simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
⊢ False
Tactic:
have i_ne_k2 : ⟨i.1, i_in_bounds⟩ ≠ k2 := by
  intro i_eq_k2
  rw [← i_eq_k2] at k2_eq_false
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li] at li_eq_true
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
⊢ False
Tactic:
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
  intro j_eq_k2
  rw [← j_eq_k2] at k2_eq_false
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li_eq_lj, li] at li_eq_true
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
⊢ False
Tactic:
by_cases ⟨i.1, i_in_bounds⟩ = k1
State after:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ⟨↑i, i_in_bounds⟩ = k1
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ⟨↑i, i_in_bounds⟩ = k1
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
. next i_eq_k1 =>
  have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
    intro j_eq_k1
    rw [← j_eq_k1] at i_eq_k1
    simp only [Fin.mk.injEq] at i_eq_k1
    exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
  specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
  simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
. next i_ne_k1 =>
  specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
  simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
⊢ ⟨↑i, i_in_bounds⟩ ≠ k2
Tactic:
intro i_eq_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
rw [← i_eq_k2] at k2_eq_false
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑i, i_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑i, i_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li] at li_eq_true
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
⊢ ⟨↑j, j_in_bounds⟩ ≠ k2
Tactic:
intro j_eq_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
⊢ False
Tactic:
rw [← j_eq_k2] at k2_eq_false
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
li_eq_lj : derivedLits.get ⟨↑i, ⋯⟩ = derivedLits.get ⟨↑j, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
li_eq_lj : derivedLits.get ⟨↑i, ⋯⟩ = derivedLits.get ⟨↑j, ⋯⟩
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k2_eq_false, li_eq_lj, li] at li_eq_true
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
next i_eq_k1 =>
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
  intro j_eq_k1
  rw [← j_eq_k1] at i_eq_k1
  simp only [Fin.mk.injEq] at i_eq_k1
  exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
  intro j_eq_k1
  rw [← j_eq_k1] at i_eq_k1
  simp only [Fin.mk.injEq] at i_eq_k1
  exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
⊢ False
Tactic:
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ ⟨↑j, j_in_bounds⟩ ≠ k1
Tactic:
intro j_eq_k1
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False
Tactic:
rw [← j_eq_k1] at i_eq_k1
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = ⟨↑j, j_in_bounds⟩
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = ⟨↑j, j_in_bounds⟩
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False
Tactic:
simp only [Fin.mk.injEq] at i_eq_k1
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
i_eq_k1 : ↑i = ↑j
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
i_eq_k1 : ↑i = ↑j
⊢ False
Tactic:
exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
State after:
no goals

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h✝ : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
next i_ne_k1 =>
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_ne_k1 : ¬⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_ne_k1 : ¬⟨↑i, i_in_bounds⟩ = k1
h3 : (derivedLits.get ⟨↑i, i_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_true : li.snd = true
i_ne_k2 : ⟨↑i, i_in_bounds⟩ ≠ k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
i_ne_k1 : ¬⟨↑i, i_in_bounds⟩ = k1
h3 : (derivedLits.get ⟨↑i, i_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
h✝ : ¬li.snd = true
⊢ False
Tactic:
next li_eq_false =>
simp only [Bool.not_eq_true] at li_eq_false
have i_ne_k1 : ⟨i.1, i_in_bounds⟩ ≠ k1 := by
  intro i_eq_k1
  rw [← i_eq_k1] at k1_eq_true
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li] at li_eq_false
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
  intro j_eq_k1
  rw [← j_eq_k1] at k1_eq_true
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li_eq_lj, li] at li_eq_false
by_cases ⟨i.1, i_in_bounds⟩ = k2
. next i_eq_k2 =>
  have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
    intro j_eq_k2
    rw [← j_eq_k2] at i_eq_k2
    simp only [Fin.mk.injEq] at i_eq_k2
    exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
  specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
  simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
. next i_ne_k2 =>
  specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
  simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : ¬li.snd = true
⊢ False
Tactic:
simp only [Bool.not_eq_true] at li_eq_false
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
⊢ False
Tactic:
have i_ne_k1 : ⟨i.1, i_in_bounds⟩ ≠ k1 := by
  intro i_eq_k1
  rw [← i_eq_k1] at k1_eq_true
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li] at li_eq_false
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
⊢ False
Tactic:
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
  intro j_eq_k1
  rw [← j_eq_k1] at k1_eq_true
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
  simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li_eq_lj, li] at li_eq_false
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
⊢ False
Tactic:
by_cases ⟨i.1, i_in_bounds⟩ = k2
State after:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ⟨↑i, i_in_bounds⟩ = k2
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ¬⟨↑i, i_in_bounds⟩ = k2
⊢ False

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ⟨↑i, i_in_bounds⟩ = k2
⊢ False

case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ¬⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
. next i_eq_k2 =>
  have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
    intro j_eq_k2
    rw [← j_eq_k2] at i_eq_k2
    simp only [Fin.mk.injEq] at i_eq_k2
    exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
  specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
  simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ¬⟨↑i, i_in_bounds⟩ = k2
⊢ False

State before:
case neg
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ¬⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
. next i_ne_k2 =>
  specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
  simp (config := { decide := true }) only [Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, derivedLits_arr_def, li] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
⊢ ⟨↑i, i_in_bounds⟩ ≠ k1
Tactic:
intro i_eq_k1
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
rw [← i_eq_k1] at k1_eq_true
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑i, i_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑i, i_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_eq_k1 : ⟨↑i, i_in_bounds⟩ = k1
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li] at li_eq_false
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
⊢ ⟨↑j, j_in_bounds⟩ ≠ k1
Tactic:
intro j_eq_k1
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False
Tactic:
rw [← j_eq_k1] at k1_eq_true
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get] at li_eq_lj
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
li_eq_lj : derivedLits.get ⟨↑i, ⋯⟩ = derivedLits.get ⟨↑j, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get ⟨↑j, j_in_bounds⟩).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_eq_k1 : ⟨↑j, j_in_bounds⟩ = k1
li_eq_lj : derivedLits.get ⟨↑i, ⋯⟩ = derivedLits.get ⟨↑j, ⋯⟩
⊢ False
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, k1_eq_true, li_eq_lj, li] at li_eq_false
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
h✝ : ⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
next i_eq_k2 =>
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
  intro j_eq_k2
  rw [← j_eq_k2] at i_eq_k2
  simp only [Fin.mk.injEq] at i_eq_k2
  exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ False
Tactic:
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
  intro j_eq_k2
  rw [← j_eq_k2] at i_eq_k2
  simp only [Fin.mk.injEq] at i_eq_k2
  exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
⊢ False
Tactic:
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
j_ne_k2 : ⟨↑j, j_in_bounds⟩ ≠ k2
h3 : (derivedLits.get ⟨↑j, j_in_bounds⟩).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
⊢ False
Tactic:
simp only [li, li_eq_lj, derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_data_get, ne_eq, not_true] at h3
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
⊢ ⟨↑j, j_in_bounds⟩ ≠ k2
Tactic:
intro j_eq_k2
State after:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f'_assignments_size : (f.performRupCheck rupHints).fst.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_satisfies_invariant :
  f.derivedLits_invariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size
    derivedLits
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
i j : Fin derivedLits_arr.size
i_ne_j : i ≠ j
li_eq_lj : derivedLits_arr[i] = derivedLits_arr[j]
li : Literal (PosFin n) := derivedLits_arr[i]
li_in_derivedLits : li ∈ derivedLits
i_in_bounds : ↑i < derivedLits.length
j_in_bounds : ↑j < derivedLits.length
k1 k2 : Fin derivedLits.length
left✝³ : (derivedLits.get k1).fst.val = ↑⟨li.fst.val, ⋯⟩
left✝² : (derivedLits.get k2).fst.val = ↑⟨li.fst.val, ⋯⟩
k1_eq_true : (derivedLits.get k1).snd = true
k2_eq_false : (derivedLits.get k2).snd = false
left✝¹ : (f.performRupCheck rupHints).fst.assignments[↑⟨li.fst.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨li.fst.val, ⋯⟩] = unassigned
h3 : ∀ (k : Fin derivedLits.length), k ≠ k1 → k ≠ k2 → (derivedLits.get k).fst.val ≠ ↑⟨li.fst.val, ⋯⟩
li_eq_false : li.snd = false
i_ne_k1 : ⟨↑i, i_in_bounds⟩ ≠ k1
j_ne_k1 : ⟨↑j, j_in_bounds⟩ ≠ k1
i_eq_k2 : ⟨↑i, i_in_bounds⟩ = k2
j_eq_k2 : ⟨↑j, j_in_bounds⟩ = k2
⊢ False