intro c c_in
α : Formula
L R : Finset Formula
C : List TNode
precond : Finset Formula
ress : List (Finset Formula)
α_in_L : α ∈ L
lrApp : LocalRuleApp (L, R) C
orule : OneSidedLocalRule precond ress
precond_eq : precond = {α}
⊢ ∀ c ∈ C, α ∈ c.1 ∨ ∃ res ∈ ress, res ⊆ c.1
α : Formula
L R : Finset Formula
C : List TNode
precond : Finset Formula
ress : List (Finset Formula)
α_in_L : α ∈ L
lrApp : LocalRuleApp (L, R) C
orule : OneSidedLocalRule precond ress
precond_eq : precond = {α}
c : TNode
c_in : c ∈ C
⊢ α ∈ c.1 ∨ ∃ res ∈ ress, res ⊆ c.1