case neg c1 =>
  simp only [fastAdmitsAux]
  right
  apply phi_ih (binders ∪ {x}) h1_right
  simp
  tauto
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 (fastReplaceFree v t phi))
no goals