case
    forall_free_in h1_1_x h1_1_phi h1_1_v h1_1_t _ _ h1_1_2 _ h1_1_ih
  | exists_free_in h1_1_x h1_1_phi h1_1_v h1_1_t _ _ h1_1_2 _ h1_1_ih =>
  right
  apply h1_1_ih
  simp
  tauto
F : Formula
v u : VarName
F' : Formula
h1_1_x : VarName
h1_1_phi : Formula
h1_1_v h1_1_t : VarName
phi'✝ : Formula
a✝¹ : isFreeIn h1_1_v (exists_ h1_1_x h1_1_phi)
h1_1_2 : ¬h1_1_x = h1_1_t
a✝ : IsSub h1_1_phi h1_1_v h1_1_t phi'✝
h1_1_ih : ∀ (binders : Finset VarName), h1_1_t ∉ binders → Rec.fastAdmitsAux h1_1_v h1_1_t binders h1_1_phi
binders : Finset VarName
h2 : h1_1_t ∉ binders
⊢ h1_1_v = h1_1_x ∨ Rec.fastAdmitsAux h1_1_v h1_1_t (binders ∪ {h1_1_x}) h1_1_phi
no goals