induction path
graph : Graph
start : Class graph
path : Path graph start
h : isCons path = true
⊢ Class.Child.class (split path h).snd = class path
case nil
graph : Graph
start x✝ : Class graph
h : isCons nil = true
⊢ Class.Child.class (split nil h).snd = class nil

case cons
graph : Graph
start start✝ : Class graph
child✝ : Class.Child start✝
a✝ : Path graph (Class.Child.class child✝)
a_ih✝ : ∀ (h : isCons a✝ = true), Class.Child.class (split a✝ h).snd = class a✝
h : isCons (cons child✝ a✝) = true
⊢ Class.Child.class (split (cons child✝ a✝) h).snd = class (cons child✝ a✝)