cases v
z : String
t v : Var
⊢ ((free_ z).subst t v).freeVarSet ⊆ t.freeVarSet ∪ v.freeVarSet \ {free_ z}
case free_
z : String
t : Var
a✝ : String
⊢ ((free_ z).subst t (free_ a✝)).freeVarSet ⊆ t.freeVarSet ∪ (free_ a✝).freeVarSet \ {free_ z}

case bound_
z : String
t : Var
a✝ : ℕ
⊢ ((free_ z).subst t (bound_ a✝)).freeVarSet ⊆ t.freeVarSet ∪ (bound_ a✝).freeVarSet \ {free_ z}