case con φ ψ =>
  cases orule'
  case con φ' ψ' =>
    simp_all
    subst c_in
    subst precond_eq
    if φ = φ' ∧ ψ = ψ'
    then
      apply Or.inr
      refine Finset.insert_subset_iff.mpr ?_
      aesop
    else aesop
  all_goals aesop
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
no goals