proposition: Lemma cfRes_sdprodK phi : K \subset cfker phi -> cfSdprod ('Res[H] phi) = phi.
proof: Proof. move=> kerK; apply/cfun_inP=> _ /(mem_sdprod defG)[x [y [Kx Hy -> _]]]. by rewrite cfSdprodE // cfResE // cfkerMl ?(subsetP kerK). 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)