Theorem: LRAT.DefaultFormula.ratAdd_result
Proof state before:
case isTrue.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✝¹ : f.ratHintsExhaustive p ratHints = true
h✝ : ¬(f.insertRupUnits c.negate).snd = true
ratAddSuccess :
  (if ((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.snd = true then
      (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, false)
    else
      if ((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.fst = true then
        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, false)
      else
        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
  . split at ratAddSuccess
    . simp at ratAddSuccess
    . 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