case pos c1 =>
  simp only [fastAdmitsAux]
  subst c1
  right
  apply not_isFreeIn_imp_fastAdmitsAux
  intro contra
  apply h1_right
  apply isFreeIn_imp_occursIn
  exact contra
v t x : VarName
phi : Formula
phi_ih :
  ∀ (binders : Finset VarName), ¬occursIn t phi → v ∉ binders → fastAdmitsAux t v binders (fastReplaceFree v t phi)
binders : Finset VarName
h2 : v ∉ binders
h1_left : t ≠ x
h1_right : ¬occursIn t phi
c1 : v = x
⊢ fastAdmitsAux t v binders (exists_ x phi)
no goals