src/HOL/Multivariate_Analysis/Fashoda.thy
changeset 56189 c4daa97ac57a
parent 56188 0268784f60da
child 56273 def3bbe6f2a5
equal deleted inserted replaced
56188:0268784f60da 56189:c4daa97ac57a
   738       apply (rule_tac[1-4] convex_box(1)[unfolded convex_contains_segment,rule_format])
   738       apply (rule_tac[1-4] convex_box(1)[unfolded convex_contains_segment,rule_format])
   739       unfolding mem_interval_cart forall_2 vector_2
   739       unfolding mem_interval_cart forall_2 vector_2
   740       using ab startfin abab assms(3)
   740       using ab startfin abab assms(3)
   741       using assms(9-)
   741       using assms(9-)
   742       unfolding assms
   742       unfolding assms
   743       apply (auto simp add: field_simps box)
   743       apply (auto simp add: field_simps box_def)
   744       done
   744       done
   745     then show "path_image ?P1 \<subseteq> cbox ?a ?b" .
   745     then show "path_image ?P1 \<subseteq> cbox ?a ?b" .
   746     have "path_image ?P2 \<subseteq> cbox ?a ?b"
   746     have "path_image ?P2 \<subseteq> cbox ?a ?b"
   747       unfolding P1P2 path_image_linepath
   747       unfolding P1P2 path_image_linepath
   748       apply (rule Un_least)+
   748       apply (rule Un_least)+
   750       apply (rule_tac[1-4] convex_box(1)[unfolded convex_contains_segment,rule_format])
   750       apply (rule_tac[1-4] convex_box(1)[unfolded convex_contains_segment,rule_format])
   751       unfolding mem_interval_cart forall_2 vector_2
   751       unfolding mem_interval_cart forall_2 vector_2
   752       using ab startfin abab assms(4)
   752       using ab startfin abab assms(4)
   753       using assms(9-)
   753       using assms(9-)
   754       unfolding assms
   754       unfolding assms
   755       apply (auto simp add: field_simps box)
   755       apply (auto simp add: field_simps box_def)
   756       done
   756       done
   757     then show "path_image ?P2 \<subseteq> cbox ?a ?b" .
   757     then show "path_image ?P2 \<subseteq> cbox ?a ?b" .
   758     show "a $ 1 - 2 = a $ 1 - 2"
   758     show "a $ 1 - 2 = a $ 1 - 2"
   759       and "b $ 1 + 2 = b $ 1 + 2"
   759       and "b $ 1 + 2 = b $ 1 + 2"
   760       and "pathstart g $ 2 - 3 = a $ 2 - 3"
   760       and "pathstart g $ 2 - 3 = a $ 2 - 3"