simp only at incrementalChecker_res
case right
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
a : Action β α
aWellFormed : wellFormedAction a
incrementalChecker_res :
  (match a with
      | Action.addEmpty id rupHints =>
        match performRupAdd f empty rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, success) else (f, rup_failure)
      | Action.addRup id c rupHints =>
        match performRupAdd f c rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.addRat id c pivot rupHints ratHints =>
        match performRatAdd f c pivot rupHints ratHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.del ids => (Formula.delete f ids, out_of_proof)).snd =
    out_of_proof
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f a).fst
⊢ unsatisfiable α f
case right
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
a : Action β α
aWellFormed : wellFormedAction a
incrementalChecker_res :
  (match a with
      | Action.addEmpty id rupHints =>
        if (performRupAdd f empty rupHints).snd = true then ((performRupAdd f empty rupHints).fst, success)
        else ((performRupAdd f empty rupHints).fst, rup_failure)
      | Action.addRup id c rupHints =>
        if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
        else ((performRupAdd f c rupHints).fst, rup_failure)
      | Action.addRat id c pivot rupHints ratHints =>
        if (performRatAdd f c pivot rupHints ratHints).snd = true then
          ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
        else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)
      | Action.del ids => (Formula.delete f ids, out_of_proof)).snd =
    out_of_proof
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f a).fst
⊢ unsatisfiable α f