diff -r 458b4e3720ab -r 27f3c10b0b50 src/ZF/ZF.thy --- a/src/ZF/ZF.thy Mon Dec 07 10:19:30 2015 +0100 +++ b/src/ZF/ZF.thy Mon Dec 07 10:23:50 2015 +0100 @@ -15,9 +15,9 @@ instance i :: "term" .. axiomatization - zero :: "i" ("0") --\the empty set\ and - Pow :: "i => i" --\power sets\ and - Inf :: "i" --\infinite set\ + zero :: "i" ("0") \\the empty set\ and + Pow :: "i => i" \\power sets\ and + Inf :: "i" \\infinite set\ text \Bounded Quantifiers\ consts @@ -56,7 +56,7 @@ Pair :: "[i, i] => i" fst :: "i => i" snd :: "i => i" - split :: "[[i, i] => 'a, i] => 'a::{}" --\for pattern-matching\ + split :: "[[i, i] => 'a, i] => 'a::{}" \\for pattern-matching\ text \Sigma and Pi Operators\ consts @@ -69,35 +69,35 @@ range :: "i => i" field :: "i => i" converse :: "i => i" - relation :: "i => o" --\recognizes sets of pairs\ - "function" :: "i => o" --\recognizes functions; can have non-pairs\ + relation :: "i => o" \\recognizes sets of pairs\ + "function" :: "i => o" \\recognizes functions; can have non-pairs\ Lambda :: "[i, i => i] => i" restrict :: "[i, i] => i" text \Infixes in order of decreasing precedence\ consts - Image :: "[i, i] => i" (infixl "``" 90) --\image\ - vimage :: "[i, i] => i" (infixl "-``" 90) --\inverse image\ - "apply" :: "[i, i] => i" (infixl "`" 90) --\function application\ - "Int" :: "[i, i] => i" (infixl "Int" 70) --\binary intersection\ - "Un" :: "[i, i] => i" (infixl "Un" 65) --\binary union\ - Diff :: "[i, i] => i" (infixl "-" 65) --\set difference\ - Subset :: "[i, i] => o" (infixl "<=" 50) --\subset relation\ + Image :: "[i, i] => i" (infixl "``" 90) \\image\ + vimage :: "[i, i] => i" (infixl "-``" 90) \\inverse image\ + "apply" :: "[i, i] => i" (infixl "`" 90) \\function application\ + "Int" :: "[i, i] => i" (infixl "Int" 70) \\binary intersection\ + "Un" :: "[i, i] => i" (infixl "Un" 65) \\binary union\ + Diff :: "[i, i] => i" (infixl "-" 65) \\set difference\ + Subset :: "[i, i] => o" (infixl "<=" 50) \\subset relation\ axiomatization - mem :: "[i, i] => o" (infixl ":" 50) --\membership relation\ + mem :: "[i, i] => o" (infixl ":" 50) \\membership relation\ abbreviation - not_mem :: "[i, i] => o" (infixl "~:" 50) --\negated membership relation\ + not_mem :: "[i, i] => o" (infixl "~:" 50) \\negated membership relation\ where "x ~: y == ~ (x : y)" abbreviation - cart_prod :: "[i, i] => i" (infixr "*" 80) --\Cartesian product\ + cart_prod :: "[i, i] => i" (infixr "*" 80) \\Cartesian product\ where "A * B == Sigma(A, %_. B)" abbreviation - function_space :: "[i, i] => i" (infixr "->" 60) --\function space\ + function_space :: "[i, i] => i" (infixr "->" 60) \\function space\ where "A -> B == Pi(A, %_. B)" @@ -616,8 +616,8 @@ declare Pow_iff [iff] -lemmas Pow_bottom = empty_subsetI [THEN PowI] --\@{term"0 \ Pow(B)"}\ -lemmas Pow_top = subset_refl [THEN PowI] --\@{term"A \ Pow(A)"}\ +lemmas Pow_bottom = empty_subsetI [THEN PowI] \\@{term"0 \ Pow(B)"}\ +lemmas Pow_top = subset_refl [THEN PowI] \\@{term"A \ Pow(A)"}\ subsection\Cantor's Theorem: There is no surjection from a set to its powerset.\