src/HOL/Deriv.thy
changeset 70346 408e15cbd2a6
parent 69593 3dda49e08b9d
     1.1 --- a/src/HOL/Deriv.thy	Fri Jun 14 08:34:27 2019 +0000
     1.2 +++ b/src/HOL/Deriv.thy	Fri Jun 14 08:34:28 2019 +0000
     1.3 @@ -1409,12 +1409,14 @@
     1.4      and dif: "\<And>x. \<lbrakk>a < x; x < b\<rbrakk> \<Longrightarrow> f differentiable (at x)"
     1.5    shows "\<exists>l z. a < z \<and> z < b \<and> DERIV f z :> l \<and> f b - f a = (b - a) * l"
     1.6  proof -
     1.7 -  obtain f' where derf: "\<And>x. \<lbrakk>a < x; x < b\<rbrakk> \<Longrightarrow> (f has_derivative f' x) (at x)"
     1.8 +  obtain f' :: "real \<Rightarrow> real \<Rightarrow> real"
     1.9 +    where derf: "\<And>x. a < x \<Longrightarrow> x < b \<Longrightarrow> (f has_derivative f' x) (at x)"
    1.10      using dif unfolding differentiable_def by metis
    1.11    then obtain z where "a < z" "z < b" "f b - f a = (f' z) (b - a)"
    1.12      using mvt [OF lt contf] by blast
    1.13    then show ?thesis
    1.14 -    by (metis derf dif has_derivative_unique has_field_derivative_imp_has_derivative linordered_field_class.sign_simps(5) real_differentiable_def)
    1.15 +    by (simp add: ac_simps)
    1.16 +      (metis derf dif has_derivative_unique has_field_derivative_imp_has_derivative real_differentiable_def)
    1.17  qed
    1.18  
    1.19  corollary MVT2: