cases r
case intro
L R : Finset Formula
c : TNode
Lcond' : Finset Formula
L_cond_in : Lcond' ⊆ L
ress : List (Finset Formula)
orule' : OneSidedLocalRule Lcond' ress
φ : Formula
c_in : ∃ a ∈ ress, (L \ Lcond' ∪ a, R) = c
α_in_L : φ ∈ L
r : ~φ = φ
⊢ φ ∈ c.1
no goals