simp_all
α : Formula
R L : Finset Formula
α_in_R : α ∈ R
c : TNode
Rcond' : Finset Formula
R_cond_in : Rcond' ⊆ R
ress : List (Finset Formula)
L_cond_in : ∅ ⊆ L
orule' : OneSidedLocalRule Rcond' ress
c_in : c ∈ applyLocalRule (LocalRule.oneSidedR orule') (L, R)
φ : Formula
precond_eq : ∀ b ∈ {φ, ~φ}, b = α
⊢ α ∈ c.2 ∨ ∃ res ∈ ∅, res ⊆ c.2
α : Formula
R L : Finset Formula
α_in_R : α ∈ R
c : TNode
Rcond' : Finset Formula
R_cond_in : Rcond' ⊆ R
ress : List (Finset Formula)
orule' : OneSidedLocalRule Rcond' ress
φ : Formula
c_in : ∃ a ∈ ress, (L, R \ Rcond' ∪ a) = c
precond_eq : φ = α ∧ ~φ = α
⊢ α ∈ c.2