proposition: Lemma double_square n: n.*2 ^2 = (n ^2) .*2 .*2.
proof: Proof. by rewrite -muln2 expnMn -[2^2]/(2 * 2) mulnA 2!muln2. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)