induction xs using Finset.induction_on
x : VarName
xs : Finset VarName
h1 : x ∈ xs
⊢ x.length ≤ finset_var_name_max_len xs
case empty
x : VarName
h1 : x ∈ ∅
⊢ x.length ≤ finset_var_name_max_len ∅

case insert
x a✝² : VarName
s✝ : Finset VarName
a✝¹ : a✝² ∉ s✝
a✝ : x ∈ s✝ → x.length ≤ finset_var_name_max_len s✝
h1 : x ∈ insert a✝² s✝
⊢ x.length ≤ finset_var_name_max_len (insert a✝² s✝)