proposition: Lemma sub_pairwise_orthogonal S1 S2 : {subset S1 <= S2} -> uniq S1 -> pairwise_orthogonal S2 -> pairwise_orthogonal S1.
proof: Proof. move=> sS12 uniqS1 /pairwise_orthogonalP[/andP[notS2_0 _] oS2]. apply/pairwise_orthogonalP; rewrite /= (contra (sS12 0)) //. by split=> //; apply: sub_in2 oS2. 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)