src/HOL/NSA/HyperNat.thy
changeset 61981 1b5845c62fa0
parent 61975 b4b11391c676
child 62378 85ed00c1fe7c
equal deleted inserted replaced
61980:6b780867d426 61981:1b5845c62fa0
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   269 subsection\<open>Existence of an infinite hypernatural number\<close>
   269 subsection\<open>Existence of an infinite hypernatural number\<close>
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   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)