Proving x >= a /\ x <= a -> x = a

Question

How would one go about proving the following

Theorem T: forall x, a: nat, x >= a /\ x <= a -> x = a.

in Coq?

Answer 1

If you don't want to use the full power of omega, I would search the standard library for the antisymmetric property of <= using SearchPattern or SearchAbout (or google) and apply le_antisym.

If you want a proof without using lemmas from the library, go by induction on x and a.