constructor
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
⊢ ((incrementalLRATChecker f a).snd = success → unsatisfiable α f) ∧
    ((incrementalLRATChecker f a).snd = out_of_proof →
      unsatisfiable α (incrementalLRATChecker f a).fst → unsatisfiable α f)
case left
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
⊢ (incrementalLRATChecker f a).snd = success → 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
⊢ (incrementalLRATChecker f a).snd = out_of_proof → unsatisfiable α (incrementalLRATChecker f a).fst → unsatisfiable α f