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
Proof state after:
case isTrue.isFalse.isFalse.isTrue
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 : (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, false) = (f', true)
⊢ f' = f.insert c

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