--- a/src/HOL/Analysis/Conformal_Mappings.thy Fri Jun 14 08:34:27 2019 +0000
+++ b/src/HOL/Analysis/Conformal_Mappings.thy Fri Jun 14 08:34:28 2019 +0000
@@ -1878,9 +1878,9 @@
apply (simp add: power2_eq_square divide_simps C_def norm_mult)
proof -
have "norm z * (norm (deriv f 0) * (r - norm z - norm z)) \<le> norm z * (norm (deriv f 0) * (r - norm z) - norm (deriv f 0) * norm z)"
- by (simp add: linordered_field_class.sign_simps(38))
+ by (simp add: sign_simps)
then show "(norm z * (r - norm z) - norm z * norm z) * norm (deriv f 0) \<le> norm (deriv f 0) * norm z * (r - norm z) - norm z * norm z * norm (deriv f 0)"
- by (simp add: linordered_field_class.sign_simps(38) mult.commute mult.left_commute)
+ by (simp add: sign_simps)
qed
qed
have sq201 [simp]: "0 < (1 - sqrt 2 / 2)" "(1 - sqrt 2 / 2) < 1"
--- a/src/HOL/Analysis/Derivative.thy Fri Jun 14 08:34:27 2019 +0000
+++ b/src/HOL/Analysis/Derivative.thy Fri Jun 14 08:34:28 2019 +0000
@@ -862,7 +862,8 @@
have "u *\<^sub>R y = u *\<^sub>R (y - x) + u *\<^sub>R x"
by (simp add: scale_right_diff_distrib)
then show "x + u *\<^sub>R (y - x) \<in> S"
- using that \<open>convex S\<close> unfolding convex_alt by (metis (no_types) atLeastAtMost_iff linordered_field_class.sign_simps(2) pth_c(3) scaleR_collapse x y)
+ using that \<open>convex S\<close> x y by (simp add: convex_alt)
+ (metis pth_b(2) pth_c(1) scaleR_collapse)
qed
have "\<And>z. z \<in> (\<lambda>u. x + u *\<^sub>R (y - x)) ` {0..1} \<Longrightarrow>
(f has_derivative f' z) (at z within (\<lambda>u. x + u *\<^sub>R (y - x)) ` {0..1})"
--- a/src/HOL/Analysis/Elementary_Normed_Spaces.thy Fri Jun 14 08:34:27 2019 +0000
+++ b/src/HOL/Analysis/Elementary_Normed_Spaces.thy Fri Jun 14 08:34:28 2019 +0000
@@ -131,8 +131,10 @@
show "\<lbrakk>\<not> 0 \<le> m; a \<le> b; x \<in> {m *\<^sub>R b + c..m *\<^sub>R a + c}\<rbrakk>
\<Longrightarrow> x \<in> (\<lambda>x. m *\<^sub>R x + c) ` {a..b}" for x
apply (rule_tac x="inverse m *\<^sub>R (x-c)" in rev_image_eqI)
- apply (auto simp: diff_le_eq neg_le_divideR_eq)
- using diff_eq_diff_less_eq linordered_field_class.sign_simps(11) minus_diff_eq not_less scaleR_le_cancel_left_neg by fastforce
+ apply (auto simp add: neg_le_divideR_eq not_le)
+ apply (auto simp: field_simps)
+ apply (metis (no_types, lifting) add_diff_cancel_left' add_le_imp_le_right diff_add_cancel inverse_eq_divide neg_le_divideR_eq neg_le_iff_le scale_minus_right)
+ done
qed
qed
qed
--- a/src/HOL/Deriv.thy Fri Jun 14 08:34:27 2019 +0000
+++ b/src/HOL/Deriv.thy Fri Jun 14 08:34:28 2019 +0000
@@ -1409,12 +1409,14 @@
and dif: "\<And>x. \<lbrakk>a < x; x < b\<rbrakk> \<Longrightarrow> f differentiable (at x)"
shows "\<exists>l z. a < z \<and> z < b \<and> DERIV f z :> l \<and> f b - f a = (b - a) * l"
proof -
- obtain f' where derf: "\<And>x. \<lbrakk>a < x; x < b\<rbrakk> \<Longrightarrow> (f has_derivative f' x) (at x)"
+ obtain f' :: "real \<Rightarrow> real \<Rightarrow> real"
+ where derf: "\<And>x. a < x \<Longrightarrow> x < b \<Longrightarrow> (f has_derivative f' x) (at x)"
using dif unfolding differentiable_def by metis
then obtain z where "a < z" "z < b" "f b - f a = (f' z) (b - a)"
using mvt [OF lt contf] by blast
then show ?thesis
- by (metis derf dif has_derivative_unique has_field_derivative_imp_has_derivative linordered_field_class.sign_simps(5) real_differentiable_def)
+ by (simp add: ac_simps)
+ (metis derf dif has_derivative_unique has_field_derivative_imp_has_derivative real_differentiable_def)
qed
corollary MVT2:
--- a/src/HOL/Library/Extended_Nonnegative_Real.thy Fri Jun 14 08:34:27 2019 +0000
+++ b/src/HOL/Library/Extended_Nonnegative_Real.thy Fri Jun 14 08:34:28 2019 +0000
@@ -1928,13 +1928,12 @@
text \<open>The next lemma is wrong for $a = top$, for $b = c = 1$ for instance.\<close>
lemma ennreal_right_diff_distrib:
- fixes a b c::ennreal
+ fixes a b c :: ennreal
assumes "a \<noteq> top"
shows "a * (b - c) = a * b - a * c"
- apply (cases a, cases b, cases c, auto simp add: assms)
- apply (metis (mono_tags, lifting) ennreal_minus ennreal_mult' linordered_field_class.sign_simps(38) split_mult_pos_le)
- apply (metis ennreal_minus_zero ennreal_mult_cancel_left ennreal_top_eq_mult_iff minus_top_ennreal mult_eq_0_iff top_neq_ennreal)
- apply (metis ennreal_minus_eq_top ennreal_minus_zero ennreal_mult_eq_top_iff mult_eq_0_iff)
+ apply (cases a; cases b; cases c)
+ apply (use assms in \<open>auto simp add: ennreal_mult_top ennreal_minus ennreal_mult' [symmetric]\<close>)
+ apply (simp add: algebra_simps)
done
lemma SUP_diff_ennreal: