equal
deleted
inserted
replaced
201 by (metis surj_def) |
201 by (metis surj_def) |
202 obtain n where n: "prod_decode n = (i,j)" using surj_prod_decode |
202 obtain n where n: "prod_decode n = (i,j)" using surj_prod_decode |
203 by (metis surj_def) |
203 by (metis surj_def) |
204 |
204 |
205 from Fract i j n show ?thesis |
205 from Fract i j n show ?thesis |
206 by (metis prod.cases prod_case_split) |
206 by (metis prod.cases) |
207 qed |
207 qed |
208 qed |
208 qed |
209 |
209 |
210 lemma rats_enumeration: "\<rat> = range (of_rat o nat_to_rat_surj)" |
210 lemma rats_enumeration: "\<rat> = range (of_rat o nat_to_rat_surj)" |
211 using nat_to_rat_surj |
211 using nat_to_rat_surj |