proposition: Lemma eq_orthonormal R S : perm_eq R S -> orthonormal R = orthonormal S.
proof: Proof. move=> eqRS; rewrite !orthonormalE (eq_all_r (perm_mem eqRS)). by rewrite (eq_pairwise_orthogonal eqRS). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)