src/ZF/Cardinal.ML
changeset 5143 b94cd208f073
parent 5137 60205b0de9b9
child 5147 825877190618
equal deleted inserted replaced
5142:c56aa8b59dc0 5143:b94cd208f073
   255 by (simp_tac (simpset() addsimps prems) 1);
   255 by (simp_tac (simpset() addsimps prems) 1);
   256 qed "Least_cong";
   256 qed "Least_cong";
   257 
   257 
   258 (*Need AC to get X lepoll Y ==> |X| le |Y|;  see well_ord_lepoll_imp_Card_le
   258 (*Need AC to get X lepoll Y ==> |X| le |Y|;  see well_ord_lepoll_imp_Card_le
   259   Converse also requires AC, but see well_ord_cardinal_eqE*)
   259   Converse also requires AC, but see well_ord_cardinal_eqE*)
   260 Goalw [eqpoll_def,cardinal_def] "!!X Y. X eqpoll Y ==> |X| = |Y|";
   260 Goalw [eqpoll_def,cardinal_def] "X eqpoll Y ==> |X| = |Y|";
   261 by (rtac Least_cong 1);
   261 by (rtac Least_cong 1);
   262 by (blast_tac (claset() addIs [comp_bij, bij_converse_bij]) 1);
   262 by (blast_tac (claset() addIs [comp_bij, bij_converse_bij]) 1);
   263 qed "cardinal_cong";
   263 qed "cardinal_cong";
   264 
   264 
   265 (*Under AC, the premise becomes trivial; one consequence is ||A|| = |A|*)
   265 (*Under AC, the premise becomes trivial; one consequence is ||A|| = |A|*)