diff -r 46f59511b7bb -r d97fdabd9e2b src/HOL/Analysis/Infinite_Sum.thy --- a/src/HOL/Analysis/Infinite_Sum.thy Fri Sep 20 19:07:10 2024 +0200 +++ b/src/HOL/Analysis/Infinite_Sum.thy Fri Sep 20 19:51:08 2024 +0200 @@ -34,40 +34,40 @@ definition HAS_SUM :: \('a \ 'b :: {comm_monoid_add, topological_space}) \ 'a set \ 'b \ bool\ where has_sum_def: \HAS_SUM f A x \ (sum f \ x) (finite_subsets_at_top A)\ -abbreviation has_sum (infixr "has'_sum" 46) where +abbreviation has_sum (infixr \has'_sum\ 46) where "(f has_sum S) A \ HAS_SUM f A S" -definition summable_on :: "('a \ 'b::{comm_monoid_add, topological_space}) \ 'a set \ bool" (infixr "summable'_on" 46) where +definition summable_on :: "('a \ 'b::{comm_monoid_add, topological_space}) \ 'a set \ bool" (infixr \summable'_on\ 46) where "f summable_on A \ (\x. (f has_sum x) A)" definition infsum :: "('a \ 'b::{comm_monoid_add,t2_space}) \ 'a set \ 'b" where "infsum f A = (if f summable_on A then Lim (finite_subsets_at_top A) (sum f) else 0)" -abbreviation abs_summable_on :: "('a \ 'b::real_normed_vector) \ 'a set \ bool" (infixr "abs'_summable'_on" 46) where +abbreviation abs_summable_on :: "('a \ 'b::real_normed_vector) \ 'a set \ bool" (infixr \abs'_summable'_on\ 46) where "f abs_summable_on A \ (\x. norm (f x)) summable_on A" syntax (ASCII) - "_infsum" :: "pttrn \ 'a set \ 'b \ 'b::topological_comm_monoid_add" ("(3INFSUM (_/:_)./ _)" [0, 51, 10] 10) + "_infsum" :: "pttrn \ 'a set \ 'b \ 'b::topological_comm_monoid_add" (\(3INFSUM (_/:_)./ _)\ [0, 51, 10] 10) syntax - "_infsum" :: "pttrn \ 'a set \ 'b \ 'b::topological_comm_monoid_add" ("(2\\<^sub>\(_/\_)./ _)" [0, 51, 10] 10) + "_infsum" :: "pttrn \ 'a set \ 'b \ 'b::topological_comm_monoid_add" (\(2\\<^sub>\(_/\_)./ _)\ [0, 51, 10] 10) syntax_consts "_infsum" \ infsum translations \ \Beware of argument permutation!\ "\\<^sub>\i\A. b" \ "CONST infsum (\i. b) A" syntax (ASCII) - "_univinfsum" :: "pttrn \ 'a \ 'a" ("(3INFSUM _./ _)" [0, 10] 10) + "_univinfsum" :: "pttrn \ 'a \ 'a" (\(3INFSUM _./ _)\ [0, 10] 10) syntax - "_univinfsum" :: "pttrn \ 'a \ 'a" ("(2\\<^sub>\_./ _)" [0, 10] 10) + "_univinfsum" :: "pttrn \ 'a \ 'a" (\(2\\<^sub>\_./ _)\ [0, 10] 10) syntax_consts "_univinfsum" \ infsum translations "\\<^sub>\x. t" \ "CONST infsum (\x. t) (CONST UNIV)" syntax (ASCII) - "_qinfsum" :: "pttrn \ bool \ 'a \ 'a" ("(3INFSUM _ |/ _./ _)" [0, 0, 10] 10) + "_qinfsum" :: "pttrn \ bool \ 'a \ 'a" (\(3INFSUM _ |/ _./ _)\ [0, 0, 10] 10) syntax - "_qinfsum" :: "pttrn \ bool \ 'a \ 'a" ("(2\\<^sub>\_ | (_)./ _)" [0, 0, 10] 10) + "_qinfsum" :: "pttrn \ bool \ 'a \ 'a" (\(2\\<^sub>\_ | (_)./ _)\ [0, 0, 10] 10) syntax_consts "_qinfsum" \ infsum translations