--- a/src/HOLCF/Sprod1.ML Thu Jun 29 16:16:24 1995 +0200
+++ b/src/HOLCF/Sprod1.ML Thu Jun 29 16:28:40 1995 +0200
@@ -14,39 +14,24 @@
qed_goalw "less_sprod1a" Sprod1.thy [less_sprod_def]
- "p1=Ispair(UU,UU) ==> less_sprod(p1,p2)"
-(fn prems =>
+ "p1=Ispair UU UU ==> less_sprod p1 p2"
+ (fn prems =>
[
(cut_facts_tac prems 1),
- (rtac eqTrueE 1),
- (rtac select_equality 1),
- (rtac conjI 1),
- (fast_tac HOL_cs 1),
- (strip_tac 1),
- (contr_tac 1),
- (dtac conjunct1 1),
- (etac rev_mp 1),
- (atac 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 =>
+ "p1~=Ispair UU UU ==> \
+\ less_sprod p1 p2 = ( Isfst p1 << Isfst p2 & Issnd p1 << Issnd p2)"
+ (fn prems =>
[
(cut_facts_tac prems 1),
- (rtac select_equality 1),
- (rtac conjI 1),
- (strip_tac 1),
- (contr_tac 1),
- (fast_tac HOL_cs 1),
- (dtac conjunct2 1),
- (etac rev_mp 1),
- (atac 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"
+ "less_sprod(Ispair x y)(Ispair UU UU) ==> x = UU | y = UU"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -55,18 +40,18 @@
(rtac disjI1 1),
(rtac antisym_less 1),
(rtac minimal 2),
- (res_inst_tac [("s","Isfst(Ispair(x,y))"),("t","x")] subst 1),
+ (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),
+ (res_inst_tac [("s","Isfst(Ispair UU UU)"),("t","UU")] subst 1),
(simp_tac Sprod_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)"
+ "less_sprod p (Ispair UU UU) ==> p = Ispair UU UU"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -78,22 +63,22 @@
]);
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"
+ "[|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),
+ (res_inst_tac [("s","Isfst(Ispair xa ya)"),("t","xa")] subst 1),
(simp_tac (Sprod_ss addsimps prems)1),
- (res_inst_tac [("s","Isfst(Ispair(x,y))"),("t","x")] subst 1),
+ (res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1),
(simp_tac (Sprod_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 (Sprod_ss addsimps prems)1),
- (res_inst_tac [("s","Issnd(Ispair(xa,ya))"),("t","ya")] subst 1),
+ (res_inst_tac [("s","Issnd(Ispair xa ya)"),("t","ya")] subst 1),
(simp_tac (Sprod_ss addsimps prems)1),
- (res_inst_tac [("s","Issnd(Ispair(x,y))"),("t","y")] subst 1),
+ (res_inst_tac [("s","Issnd(Ispair x y)"),("t","y")] subst 1),
(simp_tac (Sprod_ss addsimps prems)1),
(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct2) 1),
(resolve_tac prems 1),
@@ -105,7 +90,7 @@
(* less_sprod is a partial order on Sprod *)
(* ------------------------------------------------------------------------ *)
-qed_goal "refl_less_sprod" Sprod1.thy "less_sprod(p,p)"
+qed_goal "refl_less_sprod" Sprod1.thy "less_sprod p p"
(fn prems =>
[
(res_inst_tac [("p","p")] IsprodE 1),
@@ -118,7 +103,7 @@
qed_goal "antisym_less_sprod" Sprod1.thy
- "[|less_sprod(p1,p2);less_sprod(p2,p1)|] ==> p1=p2"
+ "[|less_sprod p1 p2;less_sprod p2 p1|] ==> p1=p2"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -146,7 +131,7 @@
]);
qed_goal "trans_less_sprod" Sprod1.thy
- "[|less_sprod(p1::'a**'b,p2);less_sprod(p2,p3)|] ==> less_sprod(p1,p3)"
+ "[|less_sprod (p1::'a**'b) p2;less_sprod p2 p3|] ==> less_sprod p1 p3"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -155,11 +140,11 @@
(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),
+ (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)")]
+ (res_inst_tac [("Q","p2=Ispair(UU::'a)(UU::'b)")]
(excluded_middle RS disjE) 1),
(rtac (defined_Ispair RS less_sprod1b RS ssubst) 1),
(REPEAT (atac 1)),
@@ -181,7 +166,7 @@
(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)")]
+ (res_inst_tac [("s","Ispair(UU::'a)(UU::'b)"),("t","Ispair x y")]
subst 1),
(etac (less_sprod2b RS sym) 1),
(atac 1)