equal
deleted
inserted
replaced
1852 lemma stable_nat: "stable |UNIV::nat set|" |
1852 lemma stable_nat: "stable |UNIV::nat set|" |
1853 using stable_natLeq card_of_nat stable_ordIso by auto |
1853 using stable_natLeq card_of_nat stable_ordIso by auto |
1854 |
1854 |
1855 text{* Below, the type of "A" is not important -- we just had to choose an appropriate |
1855 text{* Below, the type of "A" is not important -- we just had to choose an appropriate |
1856 type to make "A" possible. What is important is that arbitrarily large |
1856 type to make "A" possible. What is important is that arbitrarily large |
1857 \<not>finite sets of stable cardinality exist. *} |
1857 infinite sets of stable cardinality exist. *} |
1858 |
1858 |
1859 lemma infinite_stable_exists: |
1859 lemma infinite_stable_exists: |
1860 assumes CARD: "\<forall>r \<in> R. Card_order (r::'a rel)" |
1860 assumes CARD: "\<forall>r \<in> R. Card_order (r::'a rel)" |
1861 shows "\<exists>(A :: (nat + 'a set)set). |
1861 shows "\<exists>(A :: (nat + 'a set)set). |
1862 \<not>finite A \<and> stable |A| \<and> (\<forall>r \<in> R. r <o |A| )" |
1862 \<not>finite A \<and> stable |A| \<and> (\<forall>r \<in> R. r <o |A| )" |