induction xs generalizing ys
binders : List (VarName × VarName)
xs ys : List VarName
h1 : isAlphaEqvVarList binders xs ys
⊢ xs.length = ys.length
case nil
binders : List (VarName × VarName)
ys : List VarName
h1 : isAlphaEqvVarList binders [] ys
⊢ [].length = ys.length

case cons
binders : List (VarName × VarName)
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : ∀ (ys : List VarName), isAlphaEqvVarList binders tail✝ ys → tail✝.length = ys.length
ys : List VarName
h1 : isAlphaEqvVarList binders (head✝ :: tail✝) ys
⊢ (head✝ :: tail✝).length = ys.length