diff -r 42e9fd3ec1a3 -r 74909ecaf20a src/HOL/Hyperreal/HyperDef.thy --- a/src/HOL/Hyperreal/HyperDef.thy Thu Dec 14 22:08:35 2006 +0100 +++ b/src/HOL/Hyperreal/HyperDef.thy Thu Dec 14 22:09:26 2006 +0100 @@ -102,7 +102,7 @@ text{*Also, proof of various properties of @{term FreeUltrafilterNat}: an arbitrary free ultrafilter*} - +(* lemma FreeUltrafilterNat_Ex: "\U::nat set set. freeultrafilter U" by (rule nat_infinite [THEN freeultrafilter_Ex]) @@ -190,11 +190,12 @@ text{*One further property of our free ultrafilter*} + lemma FreeUltrafilterNat_Un: "X Un Y \ FreeUltrafilterNat ==> X \ FreeUltrafilterNat | Y \ FreeUltrafilterNat" by (auto, ultra) - +*) subsection{*Properties of @{term starrel}*} @@ -301,7 +302,7 @@ apply (simp add: omega_def) apply (simp add: star_of_def star_n_eq_iff) apply (auto simp add: real_of_nat_Suc diff_eq_eq [symmetric] - lemma_finite_omega_set [THEN FreeUltrafilterNat_finite]) + lemma_finite_omega_set [THEN FreeUltrafilterNat.finite]) done lemma hypreal_of_real_not_eq_omega: "hypreal_of_real x \ omega" @@ -320,7 +321,7 @@ lemma not_ex_hypreal_of_real_eq_epsilon: "~ (\x. hypreal_of_real x = epsilon)" by (auto simp add: epsilon_def star_of_def star_n_eq_iff - lemma_finite_epsilon_set [THEN FreeUltrafilterNat_finite]) + lemma_finite_epsilon_set [THEN FreeUltrafilterNat.finite]) lemma hypreal_of_real_not_eq_epsilon: "hypreal_of_real x \ epsilon" by (insert not_ex_hypreal_of_real_eq_epsilon, auto)