diff -r 46f59511b7bb -r d97fdabd9e2b src/HOL/Metis_Examples/Big_O.thy --- a/src/HOL/Metis_Examples/Big_O.thy Fri Sep 20 19:07:10 2024 +0200 +++ b/src/HOL/Metis_Examples/Big_O.thy Fri Sep 20 19:51:08 2024 +0200 @@ -16,7 +16,7 @@ subsection \Definitions\ -definition bigo :: "('a => 'b::linordered_idom) => ('a => 'b) set" ("(1O'(_'))") where +definition bigo :: "('a => 'b::linordered_idom) => ('a => 'b) set" (\(1O'(_'))\) where "O(f::('a => 'b)) == {h. \c. \x. \h x\ <= c * \f x\}" lemma bigo_pos_const: @@ -610,7 +610,7 @@ subsection \Less than or equal to\ -definition lesso :: "('a => 'b::linordered_idom) => ('a => 'b) => ('a => 'b)" (infixl " 'b::linordered_idom) => ('a => 'b) => ('a => 'b)" (infixl \ 70) where "f x. max (f x - g x) 0)" lemma bigo_lesseq1: "f =o O(h) \ \x. \g x\ <= \f x\ \