equal
deleted
inserted
replaced
161 (\<forall>a b. T a b \<longrightarrow> Abs a = b) \<and> (\<forall>b. T (Rep b) b) \<and> R = T OO conversep T" |
161 (\<forall>a b. T a b \<longrightarrow> Abs a = b) \<and> (\<forall>b. T (Rep b) b) \<and> R = T OO conversep T" |
162 unfolding Quotient_alt_def3 fun_eq_iff by auto |
162 unfolding Quotient_alt_def3 fun_eq_iff by auto |
163 |
163 |
164 lemma Quotient_alt_def5: |
164 lemma Quotient_alt_def5: |
165 "Quotient R Abs Rep T \<longleftrightarrow> |
165 "Quotient R Abs Rep T \<longleftrightarrow> |
166 T \<le> BNF_Util.Grp UNIV Abs \<and> BNF_Util.Grp UNIV Rep \<le> T\<inverse>\<inverse> \<and> R = T OO T\<inverse>\<inverse>" |
166 T \<le> BNF_Def.Grp UNIV Abs \<and> BNF_Def.Grp UNIV Rep \<le> T\<inverse>\<inverse> \<and> R = T OO T\<inverse>\<inverse>" |
167 unfolding Quotient_alt_def4 Grp_def by blast |
167 unfolding Quotient_alt_def4 Grp_def by blast |
168 |
168 |
169 lemma fun_quotient: |
169 lemma fun_quotient: |
170 assumes 1: "Quotient R1 abs1 rep1 T1" |
170 assumes 1: "Quotient R1 abs1 rep1 T1" |
171 assumes 2: "Quotient R2 abs2 rep2 T2" |
171 assumes 2: "Quotient R2 abs2 rep2 T2" |