src/CCL/mono.ML
author paulson
Mon Dec 07 18:26:25 1998 +0100 (1998-12-07)
changeset 6019 0e55c2fb2ebb
parent 1459 d12da312eff4
child 17456 bcf7544875b2
permissions -rw-r--r--
tidying
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(*  Title:      CCL/mono
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    ID:         $Id$
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Modified version of
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    Title:      HOL/mono
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1991  University of Cambridge
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Monotonicity of various operations
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*)
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writeln"File HOL/mono";
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val prems = goal Set.thy "A<=B ==> Union(A) <= Union(B)";
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by (cfast_tac prems 1);
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qed "Union_mono";
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val prems = goal Set.thy "[| B<=A |] ==> Inter(A) <= Inter(B)";
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by (cfast_tac prems 1);
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qed "Inter_anti_mono";
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val prems = goal Set.thy
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    "[| A<=B;  !!x. x:A ==> f(x)<=g(x) |] ==> \
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\    (UN x:A. f(x)) <= (UN x:B. g(x))";
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by (REPEAT (eresolve_tac [UN_E,ssubst] 1
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     ORELSE ares_tac ((prems RL [subsetD]) @ [subsetI,UN_I]) 1));
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qed "UN_mono";
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val prems = goal Set.thy
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    "[| B<=A;  !!x. x:A ==> f(x)<=g(x) |] ==> \
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\    (INT x:A. f(x)) <= (INT x:A. g(x))";
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by (REPEAT (ares_tac ((prems RL [subsetD]) @ [subsetI,INT_I]) 1
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     ORELSE etac INT_D 1));
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qed "INT_anti_mono";
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val prems = goal Set.thy "[| A<=C;  B<=D |] ==> A Un B <= C Un D";
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by (cfast_tac prems 1);
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qed "Un_mono";
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val prems = goal Set.thy "[| A<=C;  B<=D |] ==> A Int B <= C Int D";
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by (cfast_tac prems 1);
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qed "Int_mono";
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val prems = goal Set.thy "[| A<=B |] ==> Compl(B) <= Compl(A)";
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by (cfast_tac prems 1);
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qed "Compl_anti_mono";