have f'_readyForRupAdd : readyForRupAdd f' := by
  rw [f'_def]
  exact insert_readyForRupAdd f c f_readyForRupAdd
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
c : β
f' : σ
rupHints : Array Nat
heq : performRupAdd f c rupHints = (f', true)
restPrf : List (Action β α)
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → wellFormedAction a
ih :
  ∀ (f : σ),
    readyForRupAdd f →
      readyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → wellFormedAction a) → lratChecker f restPrf = success → unsatisfiable α f
f'_success : lratChecker f' restPrf = success
f'_def : f' = Formula.insert f c
⊢ 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
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
c : β
f' : σ
rupHints : Array Nat
heq : performRupAdd f c rupHints = (f', true)
restPrf : List (Action β α)
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → wellFormedAction a
ih :
  ∀ (f : σ),
    readyForRupAdd f →
      readyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → wellFormedAction a) → lratChecker f restPrf = success → unsatisfiable α f
f'_success : lratChecker f' restPrf = success
f'_def : f' = Formula.insert f c
f'_readyForRupAdd : readyForRupAdd f'
⊢ unsatisfiable α f