subst precond_eq
α : Formula
L R : Finset Formula
α_in_L : α ∈ L
φ φ' : Formula
precond_eq : ~~φ = α
L_cond_in : ~~φ' ∈ L
⊢ (α = φ' ∨ ¬α = ~~φ') ∨ φ = φ' ∨ ¬φ = ~~φ' ∧ φ ∈ L
L R : Finset Formula
φ φ' : Formula
L_cond_in : ~~φ' ∈ L
α_in_L : ~~φ ∈ L
⊢ (~~φ = φ' ∨ ¬~~φ = ~~φ') ∨ φ = φ' ∨ ¬φ = ~~φ' ∧ φ ∈ L