internlm/Lean-Github huggingface dataset:
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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]
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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]
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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)
Proof 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
Theorem: LRAT.DefaultFormula.derivedLits_nodup
Proof 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
Proof 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