Theorem: LRAT.DefaultFormula.clear_insertRup
Proof state before:
case assignments.intro.h₂
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
motive : Nat → Array Assignment → Prop := f.clear_insert_induction_motive ⋯ (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 (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits
        0).size =
    n
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits 0).size
hi2 : i < f.assignments.size
i_lt_n : i < n
h :
  let_fun i_lt_assignments_size := ⋯;
  let_fun i_lt_f_assignments_size := ⋯;
  let assignments_i :=
    (Array.foldl (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits
        0)[↑⟨i, i_lt_n⟩];
  let fassignments_i := f.assignments[↑⟨i, i_lt_n⟩];
  (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, i_lt_n⟩) ∨
    (∃ j b i_gt_zero,
        ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size ∧
          (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i, i_lt_n⟩, ⋯⟩, 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, 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) ∧
                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_lt_n⟩
⊢ (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits 0)[i] =
    f.assignments[i]
Tactic:
rcases h with ⟨h,_⟩
Proof state after:
case assignments.intro.h₂.inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
motive : Nat → Array Assignment → Prop := f.clear_insert_induction_motive ⋯ (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 (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits
        0).size =
    n
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits 0).size
hi2 : i < f.assignments.size
i_lt_n : i < n
h :
  (Array.foldl (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits
        0)[↑⟨i, i_lt_n⟩] =
    f.assignments[↑⟨i, i_lt_n⟩]
right✝ :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size),
    ↑j ≥ (f.insertRupUnits units).fst.rupUnits.size → (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i, i_lt_n⟩
⊢ (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits 0)[i] =
    f.assignments[i]

case assignments.intro.h₂.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
motive : Nat → Array Assignment → Prop := f.clear_insert_induction_motive ⋯ (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 (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments (f.insertRupUnits units).fst.rupUnits
        0).size =
    n
i : Nat
hi1 : i < (Array.foldl clearUnit (f.insertRupUnits units).1.assignments (f.insertRupUnits units).1.rupUnits 0).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 (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments
                  (f.insertRupUnits units).fst.rupUnits 0)[↑⟨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 (fun b => clearUnit b) (f.insertRupUnits units).fst.assignments
                      (f.insertRupUnits units).fst.rupUnits 0)[↑⟨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 0)[i] =
    f.assignments[i]