# HG changeset patch # User wenzelm # Date 958913368 -7200 # Node ID a705822f4e2a05bf2f7cfd5d92b4747d1f377eed # Parent e591fc327675948ecbabb5455d8569f303eec143 replaced {{ }} by { }; diff -r e591fc327675 -r a705822f4e2a src/HOL/Divides.thy --- a/src/HOL/Divides.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Divides.thy Sun May 21 14:49:28 2000 +0200 @@ -8,13 +8,13 @@ Divides = Arith + -(*We use the same sort for div and mod; +(*We use the same class for div and mod; moreover, dvd is defined whenever multiplication is*) axclass div < term instance - nat :: {div} + nat :: div consts div :: ['a::div, 'a] => 'a (infixl 70) diff -r e591fc327675 -r a705822f4e2a src/HOL/Integ/IntDiv.thy --- a/src/HOL/Integ/IntDiv.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Integ/IntDiv.thy Sun May 21 14:49:28 2000 +0200 @@ -53,7 +53,7 @@ else negateSnd (posDivAlg (-a,-b))" instance - int :: {div} + int :: "Divides.div" (*avoid clash with 'div' token*) defs div_def "a div b == fst (divAlg (a,b))" diff -r e591fc327675 -r a705822f4e2a src/HOL/Isar_examples/BasicLogic.thy --- a/src/HOL/Isar_examples/BasicLogic.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Isar_examples/BasicLogic.thy Sun May 21 14:49:28 2000 +0200 @@ -228,12 +228,12 @@ lemma "A & B --> B & A"; proof -; - {{; + {; assume ab: "A & B"; from ab; have a: A; ..; from ab; have b: B; ..; from b a; have "B & A"; ..; - }}; + }; thus ?thesis; .. -- {* rule \name{impI} *}; qed; diff -r e591fc327675 -r a705822f4e2a src/HOL/Isar_examples/KnasterTarski.thy --- a/src/HOL/Isar_examples/KnasterTarski.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Isar_examples/KnasterTarski.thy Sun May 21 14:49:28 2000 +0200 @@ -49,19 +49,19 @@ assume mono: "mono f"; show "f ?a = ?a"; proof -; - {{; + {; fix x; assume H: "x : ?H"; hence "?a <= x"; by (rule Inter_lower); with mono; have "f ?a <= f x"; ..; also; from H; have "... <= x"; ..; finally; have "f ?a <= x"; .; - }}; + }; hence ge: "f ?a <= ?a"; by (rule Inter_greatest); - {{; + {; also; presume "... <= f ?a"; finally (order_antisym); show ?thesis; .; - }}; + }; from mono ge; have "f (f ?a) <= f ?a"; ..; hence "f ?a : ?H"; ..; thus "?a <= f ?a"; by (rule Inter_lower); diff -r e591fc327675 -r a705822f4e2a src/HOL/Isar_examples/MultisetOrder.thy --- a/src/HOL/Isar_examples/MultisetOrder.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Isar_examples/MultisetOrder.thy Sun May 21 14:49:28 2000 +0200 @@ -67,7 +67,7 @@ proof; let ?R = "mult1 r"; let ?W = "acc ?R"; - {{; + {; fix M M0 a; assume M0: "M0 : ?W" and wf_hyp: "ALL b. (b, a) : r --> (ALL M:?W. M + {#b#} : ?W)" @@ -110,7 +110,7 @@ thus "N : ?W"; by (simp only: N); qed; qed; - }}; note tedious_reasoning = this; + }; note tedious_reasoning = this; assume wf: "wf r"; fix M; diff -r e591fc327675 -r a705822f4e2a src/HOL/Isar_examples/Puzzle.thy --- a/src/HOL/Isar_examples/Puzzle.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Isar_examples/Puzzle.thy Sun May 21 14:49:28 2000 +0200 @@ -23,7 +23,7 @@ (is "(!!x. ?H x ==> ?C x) ==> _"); proof -; assume asm: "!!x. ?H x ==> ?C x"; - {{; + {; fix k; have "ALL x. k = f x --> ?C x" (is "?Q k"); proof (rule less_induct); @@ -38,7 +38,7 @@ qed; qed; qed; - }}; + }; thus "?C x"; by simp; qed; diff -r e591fc327675 -r a705822f4e2a src/HOL/Real/HahnBanach/HahnBanach.thy --- a/src/HOL/Real/HahnBanach/HahnBanach.thy Sun May 21 14:44:01 2000 +0200 +++ b/src/HOL/Real/HahnBanach/HahnBanach.thy Sun May 21 14:49:28 2000 +0200 @@ -48,7 +48,7 @@ txt {* Define $M$ as the set of all norm-preserving extensions of $F$. *}; def M == "norm_pres_extensions E p F f"; - {{; + {; fix c; assume "c : chain M" "EX x. x:c"; txt {* Show that every non-empty chain $c$ in $M$ has an upper bound in $M$: $\Union c$ is greater that every element of the chain $c$, so $\Union c$ is an upper bound of $c$ that lies in $M$. *}; @@ -82,7 +82,7 @@ by (rule sup_norm_pres [OF _ _ a]) (simp!)+; qed; qed; - }}; + }; txt {* With Zorn's Lemma we can conclude that there is a maximal element $g$ in $M$. *}; @@ -340,7 +340,7 @@ It is even the least upper bound, because every upper bound of $M$ is also an upper bound for $\Union c$, as $\Union c\in M$) *}; - {{; + {; fix c; assume "c:chain M" "EX x. x:c"; have "Union c : M"; @@ -372,7 +372,7 @@ by (rule sup_norm_pres, rule a) (simp!)+; qed; qed; - }}; + }; txt {* According to Zorn's Lemma there is a maximal norm-preserving extension $g\in M$. *};