equal
deleted
inserted
replaced
912 show "interior S \<inter> interior m = {}" if "m \<in> r1 - p" for m |
912 show "interior S \<inter> interior m = {}" if "m \<in> r1 - p" for m |
913 proof - |
913 proof - |
914 have "interior m \<inter> interior (\<Union>p) = {}" |
914 have "interior m \<inter> interior (\<Union>p) = {}" |
915 proof (rule Int_interior_Union_intervals) |
915 proof (rule Int_interior_Union_intervals) |
916 show "\<And>T. T\<in>p \<Longrightarrow> interior m \<inter> interior T = {}" |
916 show "\<And>T. T\<in>p \<Longrightarrow> interior m \<inter> interior T = {}" |
917 by (metis DiffD1 DiffD2 that r1(1) r1(7) set_rev_mp) |
917 by (metis DiffD1 DiffD2 that r1(1) r1(7) rev_subsetD) |
918 qed (use divp in auto) |
918 qed (use divp in auto) |
919 then show "interior S \<inter> interior m = {}" |
919 then show "interior S \<inter> interior m = {}" |
920 unfolding divp by auto |
920 unfolding divp by auto |
921 qed |
921 qed |
922 qed (use r1 in auto) |
922 qed (use r1 in auto) |