src/HOL/Analysis/Conformal_Mappings.thy
changeset 69712 dc85b5b3a532
parent 69661 a03a63b81f44
child 69745 aec42cee2521
equal deleted inserted replaced
69711:82a604715919 69712:dc85b5b3a532
  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)