proposition: Lemma cfker_sum I r (P : pred I) (Phi : I -> 'CF(G)) : G :&: \bigcap_(i <- r | P i) cfker (Phi i) \subset cfker (\sum_(i <- r | P i) Phi i).
proof: Proof. elim/big_rec2: _ => [|i K psi Pi sK_psi]; first by rewrite setIT cfker_cfun0. by rewrite setICA; apply: subset_trans (setIS _ sK_psi) (cfker_add _ _). 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)