-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/Formula/RupAddResult.lean
theorem confirmRupHint_preserves_invariant_helper {n : Nat} (f : DefaultFormula n)
    (f_assignments_size : f.assignments.size = n)
    (acc : Array Assignment × CNF.Clause (PosFin n) × Bool × Bool) (hsize : acc.1.size = n)
    (l : Literal (PosFin n)) (ih : DerivedLitsInvariant f f_assignments_size acc.1 hsize acc.2.1)
    (h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true) :
    have hsize' : (Array.modify acc.1 l.1.1 (addAssignment l.snd)).size = n

Proof state:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × CNF.Clause (PosFin n) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.DerivedLitsInvariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) (Array.size_modify acc.fst l.fst.val (addAssignment l.snd)))) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin (List.length acc.snd.fst)
j_eq_i : (List.get acc.snd.fst j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (List.get acc.snd.fst j).snd f.assignments[↑i]
h2 : ¬hasAssignment (List.get acc.snd.fst j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin (List.length acc.snd.fst)), k ≠ j → (List.get acc.snd.fst k).fst.val ≠ ↑i
l' : Literal (PosFin n) := List.get acc.snd.fst j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : true ≠ l'.snd
l_eq_true : l.snd = true
l'_eq_false : l'.snd = false
⊢ ∃ j1 j2,
    ((l :: acc.snd.fst).get j1).fst.val = ↑i ∧
      ((l :: acc.snd.fst).get j2).fst.val = ↑i ∧
        ((l :: acc.snd.fst).get j1).snd = true ∧
          ((l :: acc.snd.fst).get j2).snd = false ∧
            (acc.fst.modify l.fst.val (addAssignment l.snd))[↑i] = both ∧
              f.assignments[↑i] = unassigned ∧
                ∀ (k : Fin (l :: acc.snd.fst).length), k ≠ j1 → k ≠ j2 → ((l :: acc.snd.fst).get k).fst.val ≠ ↑i

Tactic:
apply Exists.intro ⟨0, zero_in_bounds⟩

Result:
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × CNF.Clause (PosFin n) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.DerivedLitsInvariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) (Array.size_modify acc.fst l.fst.val (addAssignment l.snd)))) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin (List.length acc.snd.fst)
j_eq_i : (List.get acc.snd.fst j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (List.get acc.snd.fst j).snd f.assignments[↑i]
h2 : ¬hasAssignment (List.get acc.snd.fst j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin (List.length acc.snd.fst)), k ≠ j → (List.get acc.snd.fst k).fst.val ≠ ↑i
l' : Literal (PosFin n) := List.get acc.snd.fst j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : true ≠ l'.snd
l_eq_true : l.snd = true
l'_eq_false : l'.snd = false
⊢ ∃ j2,
    ((l :: acc.snd.fst).get ⟨0, zero_in_bounds⟩).fst.val = ↑i ∧
      ((l :: acc.snd.fst).get j2).fst.val = ↑i ∧
        ((l :: acc.snd.fst).get ⟨0, zero_in_bounds⟩).snd = true ∧
          ((l :: acc.snd.fst).get j2).snd = false ∧
            (acc.fst.modify l.fst.val (addAssignment l.snd))[↑i] = both ∧
              f.assignments[↑i] = unassigned ∧
                ∀ (k : Fin (l :: acc.snd.fst).length),
                  k ≠ ⟨0, zero_in_bounds⟩ → k ≠ j2 → ((l :: acc.snd.fst).get k).fst.val ≠ ↑i

Proof state:
case isFalse
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × CNF.Clause (PosFin n) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.DerivedLitsInvariant f_assignments_size acc.fst hsize acc.snd.fst
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) (Array.size_modify acc.fst l.fst.val (addAssignment l.snd)))) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j1 j2 : Fin (List.length acc.snd.fst)
j1_eq_i : (List.get acc.snd.fst j1).fst.val = ↑i
j2_eq_i : (List.get acc.snd.fst j2).fst.val = ↑i
j1_eq_true : (List.get acc.snd.fst j1).snd = true
j2_eq_false : (List.get acc.snd.fst j2).snd = false
h1 : acc.fst[↑i] = both
h2 : f.assignments[↑i] = unassigned
h3 : ∀ (k : Fin (List.length acc.snd.fst)), k ≠ j1 → k ≠ j2 → (List.get acc.snd.fst k).fst.val ≠ ↑i
j1_succ_in_bounds : ↑j1 + 1 < (l :: acc.snd.fst).length
j2_succ_in_bounds : ↑j2 + 1 < (l :: acc.snd.fst).length
j1_succ : Fin (l :: acc.snd.fst).length := ⟨↑j1 + 1, j1_succ_in_bounds⟩
j2_succ : Fin (l :: acc.snd.fst).length := ⟨↑j2 + 1, j2_succ_in_bounds⟩
l_eq_i : l.fst.val = ↑i
h✝ : ¬l.snd = true
h : acc.fst[l.fst.val]!.hasNegAssignment = false
⊢ False

Tactic:
simp +decide [getElem!, l_eq_i, i_in_bounds, h1, decidableGetElem?] at h

Result:
no goals

Proof state:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × CNF.Clause (PosFin n) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.DerivedLitsInvariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) (Array.size_modify acc.fst l.fst.val (addAssignment l.snd)))) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin (List.length acc.snd.fst)
j_eq_i : (List.get acc.snd.fst j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (List.get acc.snd.fst j).snd f.assignments[↑i]
h2 : ¬hasAssignment (List.get acc.snd.fst j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin (List.length acc.snd.fst)), k ≠ j → (List.get acc.snd.fst k).fst.val ≠ ↑i
l' : Literal (PosFin n) := List.get acc.snd.fst j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin (List.length acc.snd.fst + 1)
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
k'_in_bounds : k' < List.length acc.snd.fst
k'_ne_j : ⟨k', k'_in_bounds⟩ ≠ j
⊢ ¬(List.get acc.snd.fst ⟨k', ⋯⟩).fst.val = ↑i

Tactic:
exact h3 ⟨k', k'_in_bounds⟩ k'_ne_j

Result:
no goals