H-Cobordism Theorem

Definitions
Let $$X^n$$ and $$Y^n$$ be manifolds without boundary of dimension n. A cobordism $$W^{n+1}$$ between X and Y is an (n+1) dimensional manifold such that $$\partial W = X \cup Y$$. An oriented cobordism W can be said to exist between two orientable manifolds X and Y where W is a cobordism such that $$\partial W = X \cup \overline{Y}$$, where this final symbol means Y taken with reverse orientation.

If $$\forall m \in \mathbb{N}, \pi_m (W)=\pi_m (X \times [0,1])$$, that is to say, W is homotopically equivalent to the trivial cobordism on X, then W is said to be an h-cobordism.

Theorem
For any two 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