-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/Formula/RupAddResult.lean
theorem clear_insertRup {n : Nat} (f : DefaultFormula n) (f_readyForRupAdd : ReadyForRupAdd f)
    (units : CNF.Clause (PosFin n)) :
    clearRupUnits (f.insertRupUnits units).1 = f

Proof state:
case assignments.intro.h₂
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.ReadyForRupAdd
units : CNF.Clause (PosFin n)
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive ⋯ (f.insertRupUnits units).fst.rupUnits
h_base : motive 0 (f.insertRupUnits units).fst.assignments
h_inductive :
  ∀ (idx : Fin (f.insertRupUnits units).fst.rupUnits.size) (assignments : Array Assignment),
    motive (↑idx) assignments → motive (↑idx + 1) (clearUnit assignments (f.insertRupUnits units).fst.rupUnits[idx])
h_size : (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits).size = n
h :
  ∀ (i : Fin n),
    let_fun i_lt_assignments_size := ⋯;
    let_fun i_lt_f_assignments_size := ⋯;
    let assignments_i :=
      (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits)[↑i];
    let fassignments_i := f.assignments[↑i];
    (assignments_i = fassignments_i ∧
        ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size),
          ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size → (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑i) ∨
      (∃ j b i_gt_zero,
          ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
            (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑i, ⋯⟩, b) ∧
              assignments_i = addAssignment b fassignments_i ∧
                ¬hasAssignment b fassignments_i = true ∧
                  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                    ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                      k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i) ∨
        ∃ j1 j2 i_gt_zero,
          ↑j1 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
            ↑j2 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
              (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑i, ⋯⟩, true) ∧
                (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑i, ⋯⟩, false) ∧
                  assignments_i = both ∧
                    fassignments_i = unassigned ∧
                      ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                        ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                          k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits).size
hi2 : i < f.assignments.size
⊢ (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits)[i] =
    f.assignments[i]

Tactic:
have i_lt_n : i < n := by rw [← f_readyForRupAdd.2.1]; exact hi2

Result:
case assignments.intro.h₂
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.ReadyForRupAdd
units : CNF.Clause (PosFin n)
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive ⋯ (f.insertRupUnits units).fst.rupUnits
h_base : motive 0 (f.insertRupUnits units).fst.assignments
h_inductive :
  ∀ (idx : Fin (f.insertRupUnits units).fst.rupUnits.size) (assignments : Array Assignment),
    motive (↑idx) assignments → motive (↑idx + 1) (clearUnit assignments (f.insertRupUnits units).fst.rupUnits[idx])
h_size : (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits).size = n
h :
  ∀ (i : Fin n),
    let_fun i_lt_assignments_size := ⋯;
    let_fun i_lt_f_assignments_size := ⋯;
    let assignments_i :=
      (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits)[↑i];
    let fassignments_i := f.assignments[↑i];
    (assignments_i = fassignments_i ∧
        ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size),
          ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size → (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑i) ∨
      (∃ j b i_gt_zero,
          ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
            (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑i, ⋯⟩, b) ∧
              assignments_i = addAssignment b fassignments_i ∧
                ¬hasAssignment b fassignments_i = true ∧
                  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                    ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                      k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i) ∨
        ∃ j1 j2 i_gt_zero,
          ↑j1 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
            ↑j2 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
              (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑i, ⋯⟩, true) ∧
                (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑i, ⋯⟩, false) ∧
                  assignments_i = both ∧
                    fassignments_i = unassigned ∧
                      ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                        ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                          k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits).size
hi2 : i < f.assignments.size
i_lt_n : i < n
⊢ (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits)[i] =
    f.assignments[i]

Proof state:
case assignments.intro.h₂.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.ReadyForRupAdd
units : CNF.Clause (PosFin n)
motive : Nat → Array Assignment → Prop := f.ClearInsertInductionMotive ⋯ (f.insertRupUnits units).fst.rupUnits
h_base : motive 0 (f.insertRupUnits units).fst.assignments
h_inductive :
  ∀ (idx : Fin (f.insertRupUnits units).fst.rupUnits.size) (assignments : Array Assignment),
    motive (↑idx) assignments → motive (↑idx + 1) (clearUnit assignments (f.insertRupUnits units).fst.rupUnits[idx])
h_size : (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits).size = n
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits).size
hi2 : i < f.assignments.size
i_lt_n : i < n
h✝ :
  (∃ j b i_gt_zero,
      ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
        (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i, i_lt_n⟩, ⋯⟩, b) ∧
          (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments
                  (f.insertRupUnits units).fst.rupUnits)[↑⟨i, i_lt_n⟩] =
              addAssignment b f.assignments[↑⟨i, i_lt_n⟩] ∧
            ¬hasAssignment b f.assignments[↑⟨i, i_lt_n⟩] = true ∧
              ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                  k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i, i_lt_n⟩) ∨
    ∃ j1 j2 i_gt_zero,
      ↑j1 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
        ↑j2 ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
          (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i, i_lt_n⟩, ⋯⟩, true) ∧
            (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i, i_lt_n⟩, ⋯⟩, false) ∧
              (Array.foldl clearUnit (f.insertRupUnits units).fst.assignments
                      (f.insertRupUnits units).fst.rupUnits)[↑⟨i, i_lt_n⟩] =
                  both ∧
                f.assignments[↑⟨i, i_lt_n⟩] = unassigned ∧
                  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                    ↑k ≥ (f.insertRupUnits units).fst.rupUnits.size →
                      k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i, i_lt_n⟩
⊢ (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits)[i] =
    f.assignments[i]

Tactic:
omega

Result:
no goals