Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case h_2
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt✝ : Option (DefaultClause n)
c✝ : DefaultClause n
cOpt_in_arr : some c✝ ∈ arr.data
hsize : (ofArray_fold_fn acc (some c✝)).size = n
h :
  hasAssignment b
      (match c✝.isUnit with
        | none => acc
        | some (l, true) => acc.modify l.val addPosAssignment
        | some (l, false) => acc.modify l.val addNegAssignment)[i.val] =
    true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
next cOpt c =>
match heq : isUnit c with
| none =>
  simp only [heq] at h
  exact ih.2 i b h
| some (l, true) =>
  simp only [heq] at h
  have i_in_bounds : i.1 < acc.size := by simp only [ih.1, i.2.2]
  have l_in_bounds : l.1 < acc.size := by simp only [ih.1, l.2.2]
  rcases ih with ⟨hsize, ih⟩
  by_cases i = l.1
  . next i_eq_l =>
    simp only [i_eq_l, Array.get_modify_at_idx l_in_bounds] at h
    by_cases b
    . next b_eq_true =>
      rw [isUnit_iff, DefaultClause.toList] at heq
      simp only [toList, ofArray, Array.toList_eq, List.map, List.append_nil, List.mem_filterMap, id_eq, exists_eq_right]
      have i_eq_l : i = l := Subtype.ext i_eq_l
      simp only [unit, b_eq_true, i_eq_l]
      have c_def : c = ⟨c.clause, c.nodupkey, c.nodup⟩ := rfl
      simp only [heq] at c_def
      rw [c_def] at cOpt_in_arr
      exact cOpt_in_arr
    . next b_eq_false =>
      simp only [Bool.not_eq_true] at b_eq_false
      simp only [hasAssignment, b_eq_false, ite_false, hasNeg_of_addPos] at h
      specialize ih l false
      simp only [hasAssignment, ite_false] at ih
      rw [b_eq_false, Subtype.ext i_eq_l]
      exact ih h
  . next i_ne_l =>
    simp only [Array.get_modify_unchanged l_in_bounds i_in_bounds _ (Ne.symm i_ne_l)] at h
    exact ih i b h
| some (l, false) =>
  simp only [heq] at h
  have i_in_bounds : i.1 < acc.size := by simp only [ih.1, i.2.2]
  have l_in_bounds : l.1 < acc.size := by simp only [ih.1, l.2.2]
  rcases ih with ⟨hsize, ih⟩
  by_cases i = l.1
  . next i_eq_l =>
    simp only [i_eq_l, Array.get_modify_at_idx l_in_bounds] at h
    by_cases b
    . next b_eq_true =>
      simp only [hasAssignment, b_eq_true, ite_true, hasPos_of_addNeg] at h
      specialize ih l true
      simp only [hasAssignment, ite_false] at ih
      rw [b_eq_true, Subtype.ext i_eq_l]
      exact ih h
    . next b_eq_false =>
      rw [isUnit_iff, DefaultClause.toList] at heq
      simp only [toList, ofArray, Array.toList_eq, List.map, List.append_nil, List.mem_filterMap, id_eq, exists_eq_right]
      have i_eq_l : i = l := Subtype.ext i_eq_l
      simp only [unit, b_eq_false, i_eq_l]
      have c_def : c = ⟨c.clause, c.nodupkey, c.nodup⟩ := rfl
      simp only [heq] at c_def
      rw [c_def] at cOpt_in_arr
      exact cOpt_in_arr
  . next i_ne_l =>
    simp only [Array.get_modify_unchanged l_in_bounds i_in_bounds _ (Ne.symm i_ne_l)] at h
    exact ih i b h
Proof state after:
no goals