--- a/src/HOLCF/Sprod1.ML Sat Feb 15 18:24:05 1997 +0100
+++ b/src/HOLCF/Sprod1.ML Mon Feb 17 10:57:11 1997 +0100
@@ -1,183 +1,36 @@
-(* Title: HOLCF/sprod1.ML
+(* Title: HOLCF/Sprod1.ML
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
-Lemmas for theory sprod1.thy
+Lemmas for theory Sprod1.thy
*)
open Sprod1;
(* ------------------------------------------------------------------------ *)
-(* reduction properties for less_sprod *)
-(* ------------------------------------------------------------------------ *)
-
-
-qed_goalw "less_sprod1a" Sprod1.thy [less_sprod_def]
- "p1=Ispair UU UU ==> less_sprod p1 p2"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (asm_simp_tac HOL_ss 1)
- ]);
-
-qed_goalw "less_sprod1b" Sprod1.thy [less_sprod_def]
- "p1~=Ispair UU UU ==> \
-\ less_sprod p1 p2 = ( Isfst p1 << Isfst p2 & Issnd p1 << Issnd p2)"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (asm_simp_tac HOL_ss 1)
- ]);
-
-qed_goal "less_sprod2a" Sprod1.thy
- "less_sprod(Ispair x y)(Ispair UU UU) ==> x = UU | y = UU"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac (excluded_middle RS disjE) 1),
- (atac 2),
- (rtac disjI1 1),
- (rtac antisym_less 1),
- (rtac minimal 2),
- (res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1),
- (rtac Isfst 1),
- (fast_tac HOL_cs 1),
- (fast_tac HOL_cs 1),
- (res_inst_tac [("s","Isfst(Ispair UU UU)"),("t","UU")] subst 1),
- (simp_tac Sprod0_ss 1),
- (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1),
- (REPEAT (fast_tac HOL_cs 1))
- ]);
-
-qed_goal "less_sprod2b" Sprod1.thy
- "less_sprod p (Ispair UU UU) ==> p = Ispair UU UU"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (res_inst_tac [("p","p")] IsprodE 1),
- (atac 1),
- (hyp_subst_tac 1),
- (rtac strict_Ispair 1),
- (etac less_sprod2a 1)
- ]);
-
-qed_goal "less_sprod2c" Sprod1.thy
- "[|less_sprod(Ispair xa ya)(Ispair x y);\
-\ xa ~= UU ; ya ~= UU; x ~= UU ; y ~= UU |] ==> xa << x & ya << y"
-(fn prems =>
- [
- (rtac conjI 1),
- (res_inst_tac [("s","Isfst(Ispair xa ya)"),("t","xa")] subst 1),
- (simp_tac (Sprod0_ss addsimps prems)1),
- (res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1),
- (simp_tac (Sprod0_ss addsimps prems)1),
- (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1),
- (resolve_tac prems 1),
- (resolve_tac prems 1),
- (simp_tac (Sprod0_ss addsimps prems)1),
- (res_inst_tac [("s","Issnd(Ispair xa ya)"),("t","ya")] subst 1),
- (simp_tac (Sprod0_ss addsimps prems)1),
- (res_inst_tac [("s","Issnd(Ispair x y)"),("t","y")] subst 1),
- (simp_tac (Sprod0_ss addsimps prems)1),
- (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct2) 1),
- (resolve_tac prems 1),
- (resolve_tac prems 1),
- (simp_tac (Sprod0_ss addsimps prems)1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
(* less_sprod is a partial order on Sprod *)
(* ------------------------------------------------------------------------ *)
-qed_goal "refl_less_sprod" Sprod1.thy "less_sprod p p"
-(fn prems =>
- [
- (res_inst_tac [("p","p")] IsprodE 1),
- (etac less_sprod1a 1),
- (hyp_subst_tac 1),
- (stac less_sprod1b 1),
- (rtac defined_Ispair 1),
- (REPEAT (fast_tac (HOL_cs addIs [refl_less]) 1))
- ]);
-
+qed_goalw "refl_less_sprod" thy [less_sprod_def]"less (p::'a ** 'b) p"
+(fn prems => [(fast_tac (HOL_cs addIs [refl_less]) 1)]);
-qed_goal "antisym_less_sprod" Sprod1.thy
- "[|less_sprod p1 p2;less_sprod p2 p1|] ==> p1=p2"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (res_inst_tac [("p","p1")] IsprodE 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("p","p2")] IsprodE 1),
- (hyp_subst_tac 1),
- (rtac refl 1),
- (hyp_subst_tac 1),
- (rtac (strict_Ispair RS sym) 1),
- (etac less_sprod2a 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("p","p2")] IsprodE 1),
- (hyp_subst_tac 1),
- (rtac (strict_Ispair) 1),
- (etac less_sprod2a 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("x1","x"),("y1","xa"),("x","y"),("y","ya")] (arg_cong RS cong) 1),
- (rtac antisym_less 1),
- (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1),
- (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1),
- (rtac antisym_less 1),
- (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1),
- (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1)
- ]);
-
-qed_goal "trans_less_sprod" Sprod1.thy
- "[|less_sprod (p1::'a**'b) p2;less_sprod p2 p3|] ==> less_sprod p1 p3"
- (fn prems =>
+qed_goalw "antisym_less_sprod" thy [less_sprod_def]
+ "[|less (p1::'a ** 'b) p2;less p2 p1|] ==> p1=p2"
+(fn prems =>
[
(cut_facts_tac prems 1),
- (res_inst_tac [("p","p1")] IsprodE 1),
- (etac less_sprod1a 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("p","p3")] IsprodE 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("s","p2"),("t","Ispair (UU::'a)(UU::'b)")] subst 1),
- (etac less_sprod2b 1),
- (atac 1),
- (hyp_subst_tac 1),
- (res_inst_tac [("Q","p2=Ispair(UU::'a)(UU::'b)")]
- (excluded_middle RS disjE) 1),
- (stac (defined_Ispair RS less_sprod1b) 1),
- (REPEAT (atac 1)),
- (rtac conjI 1),
- (res_inst_tac [("y","Isfst(p2)")] trans_less 1),
- (rtac conjunct1 1),
- (rtac (less_sprod1b RS subst) 1),
- (rtac defined_Ispair 1),
- (REPEAT (atac 1)),
- (rtac conjunct1 1),
- (rtac (less_sprod1b RS subst) 1),
- (REPEAT (atac 1)),
- (res_inst_tac [("y","Issnd(p2)")] trans_less 1),
- (rtac conjunct2 1),
- (rtac (less_sprod1b RS subst) 1),
- (rtac defined_Ispair 1),
- (REPEAT (atac 1)),
- (rtac conjunct2 1),
- (rtac (less_sprod1b RS subst) 1),
- (REPEAT (atac 1)),
- (hyp_subst_tac 1),
- (res_inst_tac [("s","Ispair(UU::'a)(UU::'b)"),("t","Ispair x y")]
- subst 1),
- (etac (less_sprod2b RS sym) 1),
- (atac 1)
+ (rtac Sel_injective_Sprod 1),
+ (fast_tac (HOL_cs addIs [antisym_less]) 1),
+ (fast_tac (HOL_cs addIs [antisym_less]) 1)
]);
-
-
-
-
-
-
-
-
-
+qed_goalw "trans_less_sprod" thy [less_sprod_def]
+ "[|less (p1::'a**'b) p2;less p2 p3|] ==> less p1 p3"
+(fn prems =>
+ [
+ (cut_facts_tac prems 1),
+ (rtac conjI 1),
+ (fast_tac (HOL_cs addIs [trans_less]) 1),
+ (fast_tac (HOL_cs addIs [trans_less]) 1)
+ ]);