equal
deleted
inserted
replaced
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) |