proposition: Lemma eq_orthogonal R1 R2 S1 S2 : R1 =i R2 -> S1 =i S2 -> orthogonal R1 S1 = orthogonal R2 S2.
proof: Proof. move=> eqR eqS; rewrite [orthogonal _ _](eq_all_r eqR). by apply: eq_all => psi /=; apply: eq_all_r. 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)