equal
deleted
inserted
replaced
2847 proof - |
2847 proof - |
2848 have [simp]: "p' \<notin> path_image g" "p' \<notin> path_image pg" "p'\<notin>path_image cp" |
2848 have [simp]: "p' \<notin> path_image g" "p' \<notin> path_image pg" "p'\<notin>path_image cp" |
2849 using "2.prems"(8) that |
2849 using "2.prems"(8) that |
2850 apply blast |
2850 apply blast |
2851 apply (metis Diff_iff Diff_insert2 contra_subsetD pg(4) that) |
2851 apply (metis Diff_iff Diff_insert2 contra_subsetD pg(4) that) |
2852 by (meson DiffD2 cp(4) set_rev_mp subset_insertI that) |
2852 by (meson DiffD2 cp(4) rev_subsetD subset_insertI that) |
2853 have "winding_number g' p' = winding_number g p' |
2853 have "winding_number g' p' = winding_number g p' |
2854 + winding_number (pg +++ cp +++ reversepath pg) p'" unfolding g'_def |
2854 + winding_number (pg +++ cp +++ reversepath pg) p'" unfolding g'_def |
2855 apply (subst winding_number_join) |
2855 apply (subst winding_number_join) |
2856 apply (simp_all add: valid_path_imp_path) |
2856 apply (simp_all add: valid_path_imp_path) |
2857 apply (intro not_in_path_image_join) |
2857 apply (intro not_in_path_image_join) |