case ncon φ ψ =>
  simp_all
  cases orule'
  case ncon φ' ψ' =>
    simp at c_in
    subst precond_eq
    cases c_in
    case inl c_eq =>
      subst c_eq
      if φ = φ'
      then simp_all
      else aesop
    case inr c_eq =>
      subst c_eq
      if ψ = ψ'
      then simp_all
      else aesop
  all_goals aesop
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 ψ : Formula
precond_eq : {~(φ⋀ψ)} = {α}
⊢ α ∈ c.2 ∨ ∃ res ∈ [{~φ}, {~ψ}], res ⊆ c.2
no goals