Theorem: LRAT.DefaultFormula.ratAdd_result
Proof state before:
case isTrue.isFalse.isFalse.isFalse
n : Nat
f : DefaultFormula n
c : DefaultClause n
p : Literal (PosFin n)
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
f' : DefaultFormula n
f_readyForRatAdd : f.readyForRatAdd
_pc : p ∈ Clause.toList c
h✝³ : f.ratHintsExhaustive p ratHints = true
h✝² : ¬(f.insertRupUnits c.negate).snd = true
h✝¹ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.snd = true
h✝ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.fst = true
ratAddSuccess :
  (if
        (Array.foldl
              (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
              (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints 0).snd =
          false then
      ((Array.foldl
            (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
            (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints 0).fst,
        false)
    else
      ({
                clauses :=
                  (Array.foldl
                        (fun x ratHint =>
                          if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
                        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints 0).1.clauses,
                rupUnits :=
                  (Array.foldl
                        (fun x ratHint =>
                          if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
                        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints 0).1.rupUnits,
                ratUnits :=
                  (Array.foldl
                        (fun x ratHint =>
                          if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
                        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints 0).1.ratUnits,
                assignments :=
                  restoreAssignments
                    (Array.foldl
                          (fun x ratHint =>
                            if x.snd = true then x.fst.performRatCheck p.negateLiteral ratHint else (x.fst, false))
                          (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints
                          0).1.assignments
                    ((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.fst }.clearRupUnits.insert
          c,
        true)) =
    (f', true)
⊢ f' = f.insert c
Tactic:
. split at ratAddSuccess
  . simp at ratAddSuccess
  . next performRatCheck_fold_success =>
    simp only [Bool.not_eq_false] at performRatCheck_fold_success
    let fc := (insertRupUnits f (negate c)).1
    have fc_assignments_size : (insertRupUnits f (negate c)).1.assignments.size = n := by
      rw [insertRupUnits_preserves_assignments_size f (negate c)]
      exact f_readyForRatAdd.2.2.1
    simp only [performRupCheck_preserves_clauses, performRupCheck_preserves_rupUnits, performRupCheck_preserves_ratUnits,
      restoreAssignments_performRupCheck fc fc_assignments_size, Prod.mk.injEq, and_true] at ratAddSuccess
    rw [← ratAddSuccess]
    clear f' ratAddSuccess
    let performRupCheck_res := (performRupCheck (insertRupUnits f (negate c)).1 rupHints).1
    have h_performRupCheck_res : performRupCheck_res.ratUnits = #[] ∧ performRupCheck_res.assignments.size = n := by
      have hsize : performRupCheck_res.assignments.size = n := by
        rw [performRupCheck_preserves_assignments_size, insertRupUnits_preserves_assignments_size, f_readyForRatAdd.2.2.1]
      exact And.intro f_readyForRatAdd.1 hsize
    have insertRupUnits_rw : (insertRupUnits f (negate c)).1 =
      ⟨(insertRupUnits f (negate c)).1.clauses, (insertRupUnits f (negate c)).1.rupUnits,
       (insertRupUnits f (negate c)).1.ratUnits, (insertRupUnits f (negate c)).1.assignments⟩ := rfl
    simp only [performRatCheck_fold_preserves_formula performRupCheck_res h_performRupCheck_res (negateLiteral p) ratHints,
      performRupCheck_preserves_clauses, performRupCheck_preserves_rupUnits, performRupCheck_preserves_ratUnits,
      restoreAssignments_performRupCheck fc fc_assignments_size, ← insertRupUnits_rw,
      clear_insertRup f f_readyForRatAdd.2 (negate c), fc, performRupCheck_res]
Proof state after:
no goals