--- a/src/LCF/pair.ML Thu Jun 01 21:14:54 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,39 +0,0 @@
-(* Title: LCF/pair
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1992 University of Cambridge
-*)
-
-val expand_all_PROD = prove_goal (the_context ())
- "(ALL p. P(p)) <-> (ALL x y. P(<x,y>))"
- (fn _ => [rtac iffI 1, fast_tac FOL_cs 1, rtac allI 1,
- rtac (surj_pairing RS subst) 1, fast_tac FOL_cs 1]);
-
-local
-val ppair = read_instantiate [("z","p::'a*'b")] surj_pairing;
-val qpair = read_instantiate [("z","q::'a*'b")] surj_pairing;
-in
-val PROD_less = prove_goal (the_context ())
- "(p::'a*'b) << q <-> FST(p) << FST(q) & SND(p) << SND(q)"
- (fn _ => [EVERY1[rtac iffI,
- rtac conjI, etac less_ap_term, etac less_ap_term,
- rtac (ppair RS subst), rtac (qpair RS subst),
- etac conjE, rtac mono, etac less_ap_term, atac]]);
-end;
-
-val PROD_eq = prove_goal (the_context ()) "p=q <-> FST(p)=FST(q) & SND(p)=SND(q)"
- (fn _ => [rtac iffI 1, asm_simp_tac LCF_ss 1,
- rewtac eq_def,
- asm_simp_tac (LCF_ss addsimps [PROD_less]) 1]);
-
-val PAIR_less = prove_goal (the_context ()) "<a,b> << <c,d> <-> a<<c & b<<d"
- (fn _ => [simp_tac (LCF_ss addsimps [PROD_less])1]);
-
-val PAIR_eq = prove_goal (the_context ()) "<a,b> = <c,d> <-> a=c & b=d"
- (fn _ => [simp_tac (LCF_ss addsimps [PROD_eq])1]);
-
-val UU_is_UU_UU = prove_goal (the_context ()) "<UU,UU> << UU"
- (fn _ => [simp_tac (LCF_ss addsimps [PROD_less]) 1])
- RS less_UU RS sym;
-
-val LCF_ss = LCF_ss addsimps [PAIR_less,PAIR_eq,UU_is_UU_UU];