Theorem: LRAT.DefaultFormula.ratAdd_result
Proof state before:
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 :
  ({
              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)
performRatCheck_fold_success :
  (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 =
    true
fc : DefaultFormula n := (f.insertRupUnits c.negate).fst
⊢ f' = f.insert c
Tactic:
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
Proof state after:
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 :
  ({
              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)
performRatCheck_fold_success :
  (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 =
    true
fc : DefaultFormula n := (f.insertRupUnits c.negate).fst
fc_assignments_size : (f.insertRupUnits c.negate).fst.assignments.size = n
⊢ f' = f.insert c