src/HOL/Multivariate_Analysis/Integration.thy
changeset 36334 068a01b4bc56
parent 36318 3567d0571932
child 36350 bc7982c54e37
child 36359 e5c785c166b2
equal deleted inserted replaced
36333:82356c9e218a 36334:068a01b4bc56
  2179   assumes "d tagged_division_of {a..b}"
  2179   assumes "d tagged_division_of {a..b}"
  2180   shows "setsum (\<lambda>(x,l). content l) d = content({a..b})"
  2180   shows "setsum (\<lambda>(x,l). content l) d = content({a..b})"
  2181   unfolding operative_tagged_division[OF monoidal_monoid operative_content assms,THEN sym]
  2181   unfolding operative_tagged_division[OF monoidal_monoid operative_content assms,THEN sym]
  2182   apply(subst setsum_iterate) using assms by auto
  2182   apply(subst setsum_iterate) using assms by auto
  2183 
  2183 
  2184 subsection {* Finally, the integral of a constant\<forall> *}
  2184 subsection {* Finally, the integral of a constant *}
  2185 
  2185 
  2186 lemma has_integral_const[intro]:
  2186 lemma has_integral_const[intro]:
  2187   "((\<lambda>x. c) has_integral (content({a..b::real^'n}) *\<^sub>R c)) ({a..b})"
  2187   "((\<lambda>x. c) has_integral (content({a..b::real^'n}) *\<^sub>R c)) ({a..b})"
  2188   unfolding has_integral apply(rule,rule,rule_tac x="\<lambda>x. ball x 1" in exI)
  2188   unfolding has_integral apply(rule,rule,rule_tac x="\<lambda>x. ball x 1" in exI)
  2189   apply(rule,rule gauge_trivial)apply(rule,rule,erule conjE)
  2189   apply(rule,rule gauge_trivial)apply(rule,rule,erule conjE)