Theorem: LRAT.DefaultFormula.ratAdd_result
Proof state before:
case isTrue.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✝² : f.ratHintsExhaustive p ratHints = true
h✝¹ : ¬(f.insertRupUnits c.negate).snd = true
h✝ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.snd = true
ratAddSuccess :
  (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
    . 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