equal
deleted
inserted
replaced
2750 by blast |
2750 by blast |
2751 |
2751 |
2752 lemma infnorm_Max: |
2752 lemma infnorm_Max: |
2753 fixes x :: "'a::euclidean_space" |
2753 fixes x :: "'a::euclidean_space" |
2754 shows "infnorm x = Max ((\<lambda>i. \<bar>x \<bullet> i\<bar>) ` Basis)" |
2754 shows "infnorm x = Max ((\<lambda>i. \<bar>x \<bullet> i\<bar>) ` Basis)" |
2755 by (simp add: infnorm_def infnorm_set_image cSup_eq_Max del: Sup_image_eq) |
2755 by (simp add: infnorm_def infnorm_set_image cSup_eq_Max) |
2756 |
2756 |
2757 lemma infnorm_set_lemma: |
2757 lemma infnorm_set_lemma: |
2758 fixes x :: "'a::euclidean_space" |
2758 fixes x :: "'a::euclidean_space" |
2759 shows "finite {\<bar>x \<bullet> i\<bar> |i. i \<in> Basis}" |
2759 shows "finite {\<bar>x \<bullet> i\<bar> |i. i \<in> Basis}" |
2760 and "{\<bar>x \<bullet> i\<bar> |i. i \<in> Basis} \<noteq> {}" |
2760 and "{\<bar>x \<bullet> i\<bar> |i. i \<in> Basis} \<noteq> {}" |