-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/Formula/RupAddResult.lean
theorem restoreAssignments_performRupCheck {n : Nat} (f : DefaultFormula n) (f_assignments_size : f.assignments.size = n)
    (rupHints : Array Nat) :
    restoreAssignments (performRupCheck f rupHints).1.assignments (performRupCheck f rupHints).2.1
      =
    f.assignments

Proof state:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f' : DefaultFormula n := (f.performRupCheck rupHints).fst
f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : CNF.Clause (PosFin n)
derivedLits_satisfies_invariant :
  f.DerivedLitsInvariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size derivedLits
derivedLits_arr : Array (Literal (PosFin n)) := { toList := derivedLits }
derivedLits_arr_def : derivedLits_arr = { toList := derivedLits }
derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
⊢ Array.foldl clearUnit f'.assignments { toList := derivedLits } = f.assignments

Tactic:
let motive := ClearInsertInductionMotive f f_assignments_size derivedLits_arr

Result:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f' : DefaultFormula n := (f.performRupCheck rupHints).fst
f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : CNF.Clause (PosFin n)
derivedLits_satisfies_invariant :
  f.DerivedLitsInvariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size derivedLits
derivedLits_arr : Array (Literal (PosFin n)) := { toList := derivedLits }
derivedLits_arr_def : derivedLits_arr = { toList := derivedLits }
derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive f_assignments_size derivedLits_arr
⊢ Array.foldl clearUnit f'.assignments { toList := derivedLits } = f.assignments

Proof state:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
⊢ restoreAssignments (f.performRupCheck rupHints).fst.assignments (f.performRupCheck rupHints).snd.fst = f.assignments

Tactic:
rw [restoreAssignments]

Result:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
⊢ List.foldl clearUnit (f.performRupCheck rupHints).fst.assignments (f.performRupCheck rupHints).snd.fst = f.assignments

Proof state:
case intro.h₂.inr.inr.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f' : DefaultFormula n := (f.performRupCheck rupHints).fst
f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : CNF.Clause (PosFin n)
derivedLits_satisfies_invariant :
  f.DerivedLitsInvariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size derivedLits
derivedLits_arr : Array (Literal (PosFin n)) := { toList := derivedLits }
derivedLits_arr_def : derivedLits_arr = { toList := derivedLits }
derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive f_assignments_size derivedLits_arr
h_base : f.ClearInsertInductionMotive f_assignments_size derivedLits_arr 0 f'.assignments
h_inductive :
  ∀ (idx : Fin derivedLits_arr.size) (assignments : Array Assignment),
    motive (↑idx) assignments →
      f.ClearInsertInductionMotive f_assignments_size derivedLits_arr (↑idx + 1)
        (clearUnit assignments derivedLits_arr[idx])
h_size : (Array.foldl clearUnit f'.assignments derivedLits_arr).size = n
i : Nat
hi1 : i < (Array.foldl clearUnit f'.assignments { toList := derivedLits }).size
hi2✝ : i < f.assignments.size
hi2 : i < n
j1 j2 : Fin derivedLits_arr.size
i_gt_zero : ↑⟨i, hi2⟩ > 0
j1_ge_derivedLits_size : ↑j1 ≥ derivedLits_arr.size
right✝ :
  ↑j2 ≥ derivedLits_arr.size ∧
    derivedLits_arr[j1] = (⟨↑⟨i, hi2⟩, ⋯⟩, true) ∧
      derivedLits_arr[j2] = (⟨↑⟨i, hi2⟩, ⋯⟩, false) ∧
        (Array.foldl clearUnit f'.assignments derivedLits_arr)[↑⟨i, hi2⟩] = both ∧
          f.assignments[↑⟨i, hi2⟩] = unassigned ∧
            ∀ (k : Fin derivedLits_arr.size),
              ↑k ≥ derivedLits_arr.size → k ≠ j1 → k ≠ j2 → derivedLits_arr[k].fst.val ≠ ↑⟨i, hi2⟩
⊢ (Array.foldl clearUnit f'.assignments { toList := derivedLits })[i] = f.assignments[i]

Tactic:
exfalso

Result:
case intro.h₂.inr.inr.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
rupHints : Array Nat
f' : DefaultFormula n := (f.performRupCheck rupHints).fst
f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : CNF.Clause (PosFin n)
derivedLits_satisfies_invariant :
  f.DerivedLitsInvariant f_assignments_size (f.performRupCheck rupHints).fst.assignments f'_assignments_size derivedLits
derivedLits_arr : Array (Literal (PosFin n)) := { toList := derivedLits }
derivedLits_arr_def : derivedLits_arr = { toList := derivedLits }
derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive f_assignments_size derivedLits_arr
h_base : f.ClearInsertInductionMotive f_assignments_size derivedLits_arr 0 f'.assignments
h_inductive :
  ∀ (idx : Fin derivedLits_arr.size) (assignments : Array Assignment),
    motive (↑idx) assignments →
      f.ClearInsertInductionMotive f_assignments_size derivedLits_arr (↑idx + 1)
        (clearUnit assignments derivedLits_arr[idx])
h_size : (Array.foldl clearUnit f'.assignments derivedLits_arr).size = n
i : Nat
hi1 : i < (Array.foldl clearUnit f'.assignments { toList := derivedLits }).size
hi2✝ : i < f.assignments.size
hi2 : i < n
j1 j2 : Fin derivedLits_arr.size
i_gt_zero : ↑⟨i, hi2⟩ > 0
j1_ge_derivedLits_size : ↑j1 ≥ derivedLits_arr.size
right✝ :
  ↑j2 ≥ derivedLits_arr.size ∧
    derivedLits_arr[j1] = (⟨↑⟨i, hi2⟩, ⋯⟩, true) ∧
      derivedLits_arr[j2] = (⟨↑⟨i, hi2⟩, ⋯⟩, false) ∧
        (Array.foldl clearUnit f'.assignments derivedLits_arr)[↑⟨i, hi2⟩] = both ∧
          f.assignments[↑⟨i, hi2⟩] = unassigned ∧
            ∀ (k : Fin derivedLits_arr.size),
              ↑k ≥ derivedLits_arr.size → k ≠ j1 → k ≠ j2 → derivedLits_arr[k].fst.val ≠ ↑⟨i, hi2⟩
⊢ False