Theorem: BVDecide.verifyCert_correct
Proof state before:
case h_1.a
c : CNF Nat
b : LratCert
x✝ : Option (Array LRAT.IntAction)
lratProof✝ : Array LRAT.IntAction
heq✝ : LRAT.parseLRATProof (String.toUTF8 b) = some lratProof✝
h1 :
  LRAT.lratChecker (LratFormula.ofCnf c).formula
      (List.map Subtype.val
        (List.filterMap
          (fun actOpt =>
            match actOpt with
            | none => none
            | some (LRAT.Action.addEmpty id rupHints) => some ⟨LRAT.Action.addEmpty id rupHints, True.intro⟩
            | some (LRAT.Action.addRup id c_1 rupHints) => some ⟨LRAT.Action.addRup id c_1 rupHints, True.intro⟩
            | some (LRAT.Action.del ids) => some ⟨LRAT.Action.del ids, True.intro⟩
            | some (LRAT.Action.addRat id c_1 pivot rupHints ratHints) =>
              if h : pivot ∈ LRAT.Clause.toList c_1 then some ⟨LRAT.Action.addRat id c_1 pivot rupHints ratHints, ⋯⟩
              else none)
          (List.map (LRAT.intActionToDefaultClauseAction ((LratFormula.ofCnf c).numVars + 1)) lratProof✝.toList))) =
    LRAT.Result.success
h2✝ : unsatisfiable (PosFin ((LratFormula.ofCnf c).numVars + 1)) (LratFormula.ofCnf c).formula
assignment : PosFin (c.numLiterals + 1) → Bool
h2 : ¬(assignment ⊨ LRAT.DefaultFormula.ofArray (List.toArray c.lift.convertLRAT'))
h3 : CNF.eval assignment c.lift = true
lratClause : LRAT.DefaultClause ((LratFormula.ofCnf c).numVars + 1)
hlclause : lratClause ∈ LRAT.Formula.toList (LRAT.DefaultFormula.ofArray (List.toArray c.lift.convertLRAT'))
⊢ assignment ⊨ lratClause
Tactic:
simp only [LRAT.Formula.toList, LRAT.DefaultFormula.toList, LRAT.DefaultFormula.ofArray,
  CNF.convertLRAT', Array.size_toArray, List.length_map, Array.toList_eq, Array.data_toArray,
  List.map_nil, List.append_nil, List.mem_filterMap, List.mem_map, id_eq, exists_eq_right] at hlclause
Proof state after:
case h_1.a
c : CNF Nat
b : LratCert
x✝ : Option (Array LRAT.IntAction)
lratProof✝ : Array LRAT.IntAction
heq✝ : LRAT.parseLRATProof (String.toUTF8 b) = some lratProof✝
h1 :
  LRAT.lratChecker (LratFormula.ofCnf c).formula
      (List.map Subtype.val
        (List.filterMap
          (fun actOpt =>
            match actOpt with
            | none => none
            | some (LRAT.Action.addEmpty id rupHints) => some ⟨LRAT.Action.addEmpty id rupHints, True.intro⟩
            | some (LRAT.Action.addRup id c_1 rupHints) => some ⟨LRAT.Action.addRup id c_1 rupHints, True.intro⟩
            | some (LRAT.Action.del ids) => some ⟨LRAT.Action.del ids, True.intro⟩
            | some (LRAT.Action.addRat id c_1 pivot rupHints ratHints) =>
              if h : pivot ∈ LRAT.Clause.toList c_1 then some ⟨LRAT.Action.addRat id c_1 pivot rupHints ratHints, ⋯⟩
              else none)
          (List.map (LRAT.intActionToDefaultClauseAction ((LratFormula.ofCnf c).numVars + 1)) lratProof✝.toList))) =
    LRAT.Result.success
h2✝ : unsatisfiable (PosFin ((LratFormula.ofCnf c).numVars + 1)) (LratFormula.ofCnf c).formula
assignment : PosFin (c.numLiterals + 1) → Bool
h2 : ¬(assignment ⊨ LRAT.DefaultFormula.ofArray (List.toArray c.lift.convertLRAT'))
h3 : CNF.eval assignment c.lift = true
lratClause : LRAT.DefaultClause ((LratFormula.ofCnf c).numVars + 1)
hlclause :
  ∃ a,
    a ∈ c.lift ∧
      (match a.convertLRAT' with
        | some foo => some (some foo)
        | none => none) =
        some (some lratClause)
⊢ assignment ⊨ lratClause