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