src/LCF/pair.ML
author lcp
Mon, 31 Oct 1994 15:35:43 +0100
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(*  Title: 	LCF/pair
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    ID:         $Id$
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    Author: 	Tobias Nipkow
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    Copyright   1992  University of Cambridge
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Theory of ordered pairs and products
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*)
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val expand_all_PROD = prove_goal LCF.thy
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	"(ALL p. P(p)) <-> (ALL x y. P(<x,y>))"
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	(fn _ => [rtac iffI 1, fast_tac FOL_cs 1, rtac allI 1,
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		  rtac (surj_pairing RS subst) 1, fast_tac FOL_cs 1]);
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local
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val ppair = read_instantiate [("z","p::'a*'b")] surj_pairing;
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val qpair = read_instantiate [("z","q::'a*'b")] surj_pairing;
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in
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val PROD_less = prove_goal LCF.thy
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	"(p::'a*'b) << q <-> FST(p) << FST(q) & SND(p) << SND(q)"
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	(fn _ => [EVERY1[rtac iffI,
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		  rtac conjI, etac less_ap_term, etac less_ap_term,
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		  rtac (ppair RS subst), rtac (qpair RS subst),
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		  etac conjE, rtac mono, etac less_ap_term, atac]]);
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end;
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val PROD_eq = prove_goal LCF.thy "p=q <-> FST(p)=FST(q) & SND(p)=SND(q)"
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	(fn _ => [rtac iffI 1, asm_simp_tac LCF_ss 1,
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		  rewrite_goals_tac [eq_def],
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		  asm_simp_tac (LCF_ss addsimps [PROD_less]) 1]);
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val PAIR_less = prove_goal LCF.thy "<a,b> << <c,d> <-> a<<c & b<<d"
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	(fn _ => [simp_tac (LCF_ss addsimps [PROD_less])1]);
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val PAIR_eq = prove_goal LCF.thy "<a,b> = <c,d> <-> a=c & b=d"
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	(fn _ => [simp_tac (LCF_ss addsimps [PROD_eq])1]);
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val UU_is_UU_UU = prove_goal LCF.thy "<UU,UU> << UU"
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		(fn _ => [simp_tac (LCF_ss addsimps [PROD_less]) 1])
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	RS less_UU RS sym;
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val LCF_ss = LCF_ss addsimps [PAIR_less,PAIR_eq,UU_is_UU_UU];