Theorem: LRAT.DefaultFormula.performRatCheck_success_entails_c_without_negPivot
Proof state before:
n : Nat
f : DefaultFormula n
hf : f.ratUnits = #[] ∧ f.assignments_invariant
negPivot : Literal (PosFin n)
ratHint : Nat × Array Nat
c : DefaultClause n
hc : f.clauses[ratHint.fst]! = some c
p : PosFin n → Bool
pf : p ⊨ f
h✝ :
  ¬({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
              assignments := f.assignments }.insertRatUnits
          (c.delete negPivot).negate).snd =
      true
performRatCheck_success :
  ({
            clauses :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.clauses,
            rupUnits :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.rupUnits,
            ratUnits :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.ratUnits,
            assignments :=
              restoreAssignments
                (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                                assignments := f.assignments }.insertRatUnits
                            (c.delete negPivot).negate).fst.performRupCheck
                      ratHint.snd).1.assignments
                (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                                assignments := f.assignments }.insertRatUnits
                            (c.delete negPivot).negate).fst.performRupCheck
                      ratHint.snd).2.fst }.clearRatUnits,
        true).snd =
    true
h :
  (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                        assignments := f.assignments }.insertRatUnits
                    (c.delete negPivot).negate).fst.performRupCheck
              ratHint.snd).2.2.snd =
      false ∧
    (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                        assignments := f.assignments }.insertRatUnits
                    (c.delete negPivot).negate).fst.performRupCheck
              ratHint.snd).2.2.fst =
      true
⊢ p ⊨ c.delete negPivot
Tactic:
have pfc := performRupCheck_of_insertRat_entails_safe_insert f hf (DefaultClause.delete c negPivot) ratHint.2 h.2 p pf
Proof state after:
n : Nat
f : DefaultFormula n
hf : f.ratUnits = #[] ∧ f.assignments_invariant
negPivot : Literal (PosFin n)
ratHint : Nat × Array Nat
c : DefaultClause n
hc : f.clauses[ratHint.fst]! = some c
p : PosFin n → Bool
pf : p ⊨ f
h✝ :
  ¬({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
              assignments := f.assignments }.insertRatUnits
          (c.delete negPivot).negate).snd =
      true
performRatCheck_success :
  ({
            clauses :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.clauses,
            rupUnits :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.rupUnits,
            ratUnits :=
              (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                              assignments := f.assignments }.insertRatUnits
                          (c.delete negPivot).negate).fst.performRupCheck
                    ratHint.snd).1.ratUnits,
            assignments :=
              restoreAssignments
                (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                                assignments := f.assignments }.insertRatUnits
                            (c.delete negPivot).negate).fst.performRupCheck
                      ratHint.snd).1.assignments
                (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                                assignments := f.assignments }.insertRatUnits
                            (c.delete negPivot).negate).fst.performRupCheck
                      ratHint.snd).2.fst }.clearRatUnits,
        true).snd =
    true
h :
  (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                        assignments := f.assignments }.insertRatUnits
                    (c.delete negPivot).negate).fst.performRupCheck
              ratHint.snd).2.2.snd =
      false ∧
    (({ clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                        assignments := f.assignments }.insertRatUnits
                    (c.delete negPivot).negate).fst.performRupCheck
              ratHint.snd).2.2.fst =
      true
pfc : p ⊨ f.insert (c.delete negPivot)
⊢ p ⊨ c.delete negPivot