src/HOL/Algebra/Group.thy
changeset 61565 352c73a689da
parent 61384 9f5145281888
child 61628 8dd2bd4fe30b
equal deleted inserted replaced
61564:6d513469f9b2 61565:352c73a689da
   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"