proposition: Lemma cpow0x a: a <> \0c -> \0c ^c a = \0c.
proof: Proof. move => /nonemptyP [x xa];rewrite - cprod_of_same. apply: cprod_eq0; exists x; aw;trivial; rewrite LgV //; exact: cardinal_set0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)