simp_all
α : Formula
L R : Finset Formula
α_in_L : α ∈ L
c : TNode
Lcond' : Finset Formula
L_cond_in : Lcond' ⊆ L
ress : List (Finset Formula)
orule' : OneSidedLocalRule Lcond' ress
R_cond_in : ∅ ⊆ R
c_in : c ∈ applyLocalRule (LocalRule.oneSidedL orule') (L, R)
φ ψ : Formula
precond_eq : {~(φ⋀ψ)} = {α}
⊢ α ∈ c.1 ∨ ∃ res ∈ [{~φ}, {~ψ}], res ⊆ c.1
α : Formula
L R : Finset Formula
α_in_L : α ∈ L
c : TNode
Lcond' : Finset Formula
L_cond_in : Lcond' ⊆ L
ress : List (Finset Formula)
orule' : OneSidedLocalRule Lcond' ress
φ ψ : Formula
c_in : ∃ a ∈ ress, (L \ Lcond' ∪ a, R) = c
precond_eq : ~(φ⋀ψ) = α
⊢ α ∈ c.1 ∨ ~φ ∈ c.1 ∨ ~ψ ∈ c.1