equal
deleted
inserted
replaced
185 by (etac (rewrite_rule [inj_on_def] finite_imageD) 1); |
185 by (etac (rewrite_rule [inj_on_def] finite_imageD) 1); |
186 by (simp_tac (simpset() addsplits [split_split]) 1); |
186 by (simp_tac (simpset() addsplits [split_split]) 1); |
187 by (etac finite_imageI 1); |
187 by (etac finite_imageI 1); |
188 by (simp_tac (simpset() addsimps [converse_def,image_def]) 1); |
188 by (simp_tac (simpset() addsimps [converse_def,image_def]) 1); |
189 by Auto_tac; |
189 by Auto_tac; |
190 by (rtac bexI 1); |
190 by (rtac bexI 1); |
191 by (assume_tac 2); |
191 by (assume_tac 2); |
192 by (Simp_tac 1); |
192 by (Simp_tac 1); |
193 qed "finite_converse"; |
193 qed "finite_converse"; |
194 AddIffs [finite_converse]; |
194 AddIffs [finite_converse]; |
195 |
195 |
196 section "Finite cardinality -- 'card'"; |
196 section "Finite cardinality -- 'card'"; |