src/HOL/Algebra/AbelCoset.thy
changeset 28823 dcbef866c9e2
parent 27717 21bbd410ba04
child 29237 e90d9d51106b
equal deleted inserted replaced
28822:7ca11ecbc4fb 28823:dcbef866c9e2
   232 proof -
   232 proof -
   233   interpret normal ["H" "\<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>"]
   233   interpret normal ["H" "\<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>"]
   234   by (rule a_normal)
   234   by (rule a_normal)
   235 
   235 
   236   show "abelian_subgroup H G"
   236   show "abelian_subgroup H G"
   237   by (unfold_locales, simp add: a_comm)
   237   proof qed (simp add: a_comm)
   238 qed
   238 qed
   239 
   239 
   240 lemma abelian_subgroupI2:
   240 lemma abelian_subgroupI2:
   241   fixes G (structure)
   241   fixes G (structure)
   242   assumes a_comm_group: "comm_group \<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>"
   242   assumes a_comm_group: "comm_group \<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>"
   547     done
   547     done
   548 qed
   548 qed
   549 
   549 
   550 lemma (in abelian_group_hom) is_abelian_group_hom:
   550 lemma (in abelian_group_hom) is_abelian_group_hom:
   551   "abelian_group_hom G H h"
   551   "abelian_group_hom G H h"
   552 by (unfold_locales)
   552   ..
   553 
   553 
   554 lemma (in abelian_group_hom) hom_add [simp]:
   554 lemma (in abelian_group_hom) hom_add [simp]:
   555   "[| x : carrier G; y : carrier G |]
   555   "[| x : carrier G; y : carrier G |]
   556         ==> h (x \<oplus>\<^bsub>G\<^esub> y) = h x \<oplus>\<^bsub>H\<^esub> h y"
   556         ==> h (x \<oplus>\<^bsub>G\<^esub> y) = h x \<oplus>\<^bsub>H\<^esub> h y"
   557 by (rule group_hom.hom_mult[OF a_group_hom,
   557 by (rule group_hom.hom_mult[OF a_group_hom,