split
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
action : Action β α
restPrf : List (Action β α)
ih :
  ∀ (f : σ),
    readyForRupAdd f →
      readyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → wellFormedAction a) → lratChecker f restPrf = success → unsatisfiable α f
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
actionWellFormed : wellFormedAction action
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → wellFormedAction a
prf✝ : List (Action β α)
id : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
restPrf' : List (Action β α)
hprf : action :: restPrf = Action.addRat id c pivot rupHints ratHints :: restPrf'
⊢ (match performRatAdd f c pivot rupHints ratHints with
      | (f, checkSuccess) => if checkSuccess = true then lratChecker f restPrf' else rup_failure) =
      success →
    unsatisfiable α f
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
action : Action β α
restPrf : List (Action β α)
ih :
  ∀ (f : σ),
    readyForRupAdd f →
      readyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → wellFormedAction a) → lratChecker f restPrf = success → unsatisfiable α f
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
actionWellFormed : wellFormedAction action
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → wellFormedAction a
prf✝ : List (Action β α)
id : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
restPrf' : List (Action β α)
hprf : action :: restPrf = Action.addRat id c pivot rupHints ratHints :: restPrf'
x✝ : σ × Bool
f✝ : σ
checkSuccess✝ : Bool
heq✝ : performRatAdd f c pivot rupHints ratHints = (f✝, checkSuccess✝)
⊢ (if checkSuccess✝ = true then lratChecker f✝ restPrf' else rup_failure) = success → unsatisfiable α f