H-Cobordism Theorem

Theorem
For any two simply connected manifolds $$X^n, Y^n \ $$, if $$n \ge 5$$ and $$\exists W$$ such that W is an h-cobordism between X and Y, then $$\exists \psi : W \rightarrow X \times [0,1]$$ such that $$\psi$$ is a diffeomorphism. In particular, X and Y are diffemorphic.

Proof
In progress