simp_all
α : Formula
L R : Finset Formula
α_in_L : α ∈ L
c : TNode
R_cond_in : ∅ ⊆ R
φ ψ : Formula
precond_eq : {φ⋀ψ} = {α}
φ' ψ' : Formula
L_cond_in : {φ'⋀ψ'} ⊆ L
c_in : c ∈ applyLocalRule (LocalRule.oneSidedL (OneSidedLocalRule.con φ' ψ')) (L, R)
⊢ α ∈ c.1 ∨ ∃ res ∈ [{φ, ψ}], res ⊆ c.1
α : Formula
L R : Finset Formula
α_in_L : α ∈ L
c : TNode
φ ψ φ' ψ' : Formula
precond_eq : φ⋀ψ = α
L_cond_in : φ'⋀ψ' ∈ L
c_in : c = (insert φ' (insert ψ' (L.erase (φ'⋀ψ'))), R)
⊢ (α = φ' ∨ α = ψ' ∨ ¬α = φ'⋀ψ') ∨ {φ, ψ} ⊆ insert φ' (insert ψ' (L.erase (φ'⋀ψ')))