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
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
Proof 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