equal
deleted
inserted
replaced
611 by (auto simp add: iso_def hom_def inj_on_def bij_betw_def) |
611 by (auto simp add: iso_def hom_def inj_on_def bij_betw_def) |
612 |
612 |
613 |
613 |
614 text\<open>Basis for homomorphism proofs: we assume two groups @{term G} and |
614 text\<open>Basis for homomorphism proofs: we assume two groups @{term G} and |
615 @{term H}, with a homomorphism @{term h} between them\<close> |
615 @{term H}, with a homomorphism @{term h} between them\<close> |
616 locale group_hom = G: group G + H: group H for G (structure) and H (structure) + |
616 locale group_hom = G?: group G + H?: group H for G (structure) and H (structure) + |
617 fixes h |
617 fixes h |
618 assumes homh: "h \<in> hom G H" |
618 assumes homh: "h \<in> hom G H" |
619 |
619 |
620 lemma (in group_hom) hom_mult [simp]: |
620 lemma (in group_hom) hom_mult [simp]: |
621 "[| x \<in> carrier G; y \<in> carrier G |] ==> h (x \<otimes>\<^bsub>G\<^esub> y) = h x \<otimes>\<^bsub>H\<^esub> h y" |
621 "[| x \<in> carrier G; y \<in> carrier G |] ==> h (x \<otimes>\<^bsub>G\<^esub> y) = h x \<otimes>\<^bsub>H\<^esub> h y" |