src/HOL/Analysis/Polytope.thy
changeset 73932 fd21b4a93043
parent 72569 d56e4eeae967
child 74513 67d87d224e00
--- a/src/HOL/Analysis/Polytope.thy	Fri Jun 18 15:03:12 2021 +0200
+++ b/src/HOL/Analysis/Polytope.thy	Thu Jul 08 08:42:36 2021 +0200
@@ -2729,7 +2729,7 @@
         using \<open>T \<subseteq> S\<close> by blast
       then have "\<exists>y\<in>S. x \<in> convex hull (S - {y})"
         using True affine_independent_iff_card [of S]
-        by (metis (no_types, hide_lams) Diff_eq_empty_iff Diff_insert0 \<open>a \<notin> T\<close> \<open>T \<subseteq> S\<close> \<open>x \<in> convex hull T\<close> hull_mono insert_Diff_single subsetCE)
+        by (metis (no_types, opaque_lifting) Diff_eq_empty_iff Diff_insert0 \<open>a \<notin> T\<close> \<open>T \<subseteq> S\<close> \<open>x \<in> convex hull T\<close> hull_mono insert_Diff_single subsetCE)
     } note * = this
     have 1: "convex hull S \<subseteq> (\<Union> a\<in>S. convex hull (S - {a}))"
       by (subst caratheodory_aff_dim) (blast dest: *)
@@ -3044,7 +3044,7 @@
   by (simp add: polytope_imp_polyhedron simplex_imp_polytope)
 
 lemma simplex_dim_ge: "n simplex S \<Longrightarrow> -1 \<le> n"
-  by (metis (no_types, hide_lams) aff_dim_geq affine_independent_iff_card diff_add_cancel diff_diff_eq2 simplex_def)
+  by (metis (no_types, opaque_lifting) aff_dim_geq affine_independent_iff_card diff_add_cancel diff_diff_eq2 simplex_def)
 
 lemma simplex_empty [simp]: "n simplex {} \<longleftrightarrow> n = -1"
 proof