equal
deleted
inserted
replaced
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|*) |