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267 |
267 |
268 |
268 |
269 subsection\<open>Existence of an infinite hypernatural number\<close> |
269 subsection\<open>Existence of an infinite hypernatural number\<close> |
270 |
270 |
271 definition |
271 definition |
272 (* omega is in fact an infinite hypernatural number = [<1,2,3,...>] *) |
272 (* \<omega> is in fact an infinite hypernatural number = [<1,2,3,...>] *) |
273 whn :: hypnat where |
273 whn :: hypnat where |
274 hypnat_omega_def: "whn = star_n (%n::nat. n)" |
274 hypnat_omega_def: "whn = star_n (%n::nat. n)" |
275 |
275 |
276 lemma hypnat_of_nat_neq_whn: "hypnat_of_nat n \<noteq> whn" |
276 lemma hypnat_of_nat_neq_whn: "hypnat_of_nat n \<noteq> whn" |
277 by (simp add: FreeUltrafilterNat.singleton' hypnat_omega_def star_of_def star_n_eq_iff) |
277 by (simp add: FreeUltrafilterNat.singleton' hypnat_omega_def star_of_def star_n_eq_iff) |