src/HOL/Analysis/Henstock_Kurzweil_Integration.thy
changeset 69597 ff784d5a5bfb
parent 69529 4ab9657b3257
child 69661 a03a63b81f44
equal deleted inserted replaced
69596:c8a2755bf220 69597:ff784d5a5bfb
   488 lemma has_integral_mult_left:
   488 lemma has_integral_mult_left:
   489   fixes c :: "_ :: real_normed_algebra"
   489   fixes c :: "_ :: real_normed_algebra"
   490   shows "(f has_integral y) S \<Longrightarrow> ((\<lambda>x. f x * c) has_integral (y * c)) S"
   490   shows "(f has_integral y) S \<Longrightarrow> ((\<lambda>x. f x * c) has_integral (y * c)) S"
   491   using has_integral_linear[OF _ bounded_linear_mult_left] by (simp add: comp_def)
   491   using has_integral_linear[OF _ bounded_linear_mult_left] by (simp add: comp_def)
   492 
   492 
   493 text\<open>The case analysis eliminates the condition @{term "f integrable_on S"} at the cost
   493 text\<open>The case analysis eliminates the condition \<^term>\<open>f integrable_on S\<close> at the cost
   494      of the type class constraint \<open>division_ring\<close>\<close>
   494      of the type class constraint \<open>division_ring\<close>\<close>
   495 corollary integral_mult_left [simp]:
   495 corollary integral_mult_left [simp]:
   496   fixes c:: "'a::{real_normed_algebra,division_ring}"
   496   fixes c:: "'a::{real_normed_algebra,division_ring}"
   497   shows "integral S (\<lambda>x. f x * c) = integral S f * c"
   497   shows "integral S (\<lambda>x. f x * c) = integral S f * c"
   498 proof (cases "f integrable_on S \<or> c = 0")
   498 proof (cases "f integrable_on S \<or> c = 0")