cases h2
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h2 : ¬v = x ∧ isFreeIn v phi
h3 : v ∉ binders
⊢ u ∉ binders
case intro
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
left✝ : ¬v = x
right✝ : isFreeIn v phi
⊢ u ∉ binders