--- a/src/HOLCF/Sprod2.ML Tue Jul 04 14:58:40 2000 +0200
+++ b/src/HOLCF/Sprod2.ML Tue Jul 04 15:58:11 2000 +0200
@@ -3,138 +3,108 @@
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
-Lemmas for Sprod2.thy
+Class Instance **::(pcpo,pcpo)po
*)
-open Sprod2;
-
(* for compatibility with old HOLCF-Version *)
-qed_goal "inst_sprod_po" thy "(op <<)=(%x y. Isfst x<<Isfst y&Issnd x<<Issnd y)"
- (fn prems =>
- [
- (fold_goals_tac [less_sprod_def]),
- (rtac refl 1)
- ]);
+val prems = goal thy "(op <<)=(%x y. Isfst x<<Isfst y&Issnd x<<Issnd y)";
+by (fold_goals_tac [less_sprod_def]);
+by (rtac refl 1);
+qed "inst_sprod_po";
(* ------------------------------------------------------------------------ *)
(* type sprod is pointed *)
(* ------------------------------------------------------------------------ *)
-qed_goal "minimal_sprod" thy "Ispair UU UU << p"
-(fn prems =>
- [
- (simp_tac(Sprod0_ss addsimps[inst_sprod_po,minimal])1)
- ]);
+val prems = goal thy "Ispair UU UU << p";
+by (simp_tac(Sprod0_ss addsimps[inst_sprod_po,minimal])1);
+qed "minimal_sprod";
bind_thm ("UU_sprod_def",minimal_sprod RS minimal2UU RS sym);
-qed_goal "least_sprod" thy "? x::'a**'b.!y. x<<y"
-(fn prems =>
- [
- (res_inst_tac [("x","Ispair UU UU")] exI 1),
- (rtac (minimal_sprod RS allI) 1)
- ]);
+val prems = goal thy "? x::'a**'b.!y. x<<y";
+by (res_inst_tac [("x","Ispair UU UU")] exI 1);
+by (rtac (minimal_sprod RS allI) 1);
+qed "least_sprod";
(* ------------------------------------------------------------------------ *)
(* Ispair is monotone in both arguments *)
(* ------------------------------------------------------------------------ *)
-qed_goalw "monofun_Ispair1" Sprod2.thy [monofun] "monofun(Ispair)"
-(fn prems =>
- [
- (strip_tac 1),
- (rtac (less_fun RS iffD2) 1),
- (strip_tac 1),
- (res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1),
- (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
- (ftac notUU_I 1),
- (atac 1),
- (REPEAT(asm_simp_tac(Sprod0_ss
- addsimps[inst_sprod_po,refl_less,minimal]) 1))
- ]);
+val prems = goalw Sprod2.thy [monofun] "monofun(Ispair)";
+by (strip_tac 1);
+by (rtac (less_fun RS iffD2) 1);
+by (strip_tac 1);
+by (res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1);
+by (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1);
+by (ftac notUU_I 1);
+by (atac 1);
+by (REPEAT(asm_simp_tac(Sprod0_ss addsimps[inst_sprod_po,refl_less,minimal]) 1));
+qed "monofun_Ispair1";
-qed_goalw "monofun_Ispair2" Sprod2.thy [monofun] "monofun(Ispair(x))"
-(fn prems =>
- [
- (strip_tac 1),
- (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
- (res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1),
- (ftac notUU_I 1),
- (atac 1),
- (REPEAT(asm_simp_tac(Sprod0_ss
- addsimps[inst_sprod_po,refl_less,minimal]) 1))
- ]);
-
+val prems = goalw Sprod2.thy [monofun] "monofun(Ispair(x))";
+by (strip_tac 1);
+by (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1);
+by (res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1);
+by (ftac notUU_I 1);
+by (atac 1);
+by (REPEAT(asm_simp_tac(Sprod0_ss addsimps[inst_sprod_po,refl_less,minimal]) 1));
+qed "monofun_Ispair2";
-qed_goal "monofun_Ispair" Sprod2.thy
- "[|x1<<x2; y1<<y2|] ==> Ispair x1 y1 << Ispair x2 y2"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac trans_less 1),
- (rtac (monofun_Ispair1 RS monofunE RS spec RS spec RS mp RS
- (less_fun RS iffD1 RS spec)) 1),
- (rtac (monofun_Ispair2 RS monofunE RS spec RS spec RS mp) 2),
- (atac 1),
- (atac 1)
- ]);
-
+Goal "[|x1<<x2; y1<<y2|] ==> Ispair x1 y1 << Ispair x2 y2";
+by (rtac trans_less 1);
+by (rtac (monofun_Ispair1 RS monofunE RS spec RS spec RS mp RS
+ (less_fun RS iffD1 RS spec)) 1);
+by (rtac (monofun_Ispair2 RS monofunE RS spec RS spec RS mp) 2);
+by (atac 1);
+by (atac 1);
+qed "monofun_Ispair";
(* ------------------------------------------------------------------------ *)
(* Isfst and Issnd are monotone *)
(* ------------------------------------------------------------------------ *)
-qed_goalw "monofun_Isfst" Sprod2.thy [monofun] "monofun(Isfst)"
-(fn prems => [(simp_tac (HOL_ss addsimps [inst_sprod_po]) 1)]);
+val prems = goalw Sprod2.thy [monofun] "monofun(Isfst)";
+by (simp_tac (HOL_ss addsimps [inst_sprod_po]) 1);
+qed "monofun_Isfst";
-qed_goalw "monofun_Issnd" Sprod2.thy [monofun] "monofun(Issnd)"
-(fn prems => [(simp_tac (HOL_ss addsimps [inst_sprod_po]) 1)]);
+val prems = goalw Sprod2.thy [monofun] "monofun(Issnd)";
+by (simp_tac (HOL_ss addsimps [inst_sprod_po]) 1);
+qed "monofun_Issnd";
(* ------------------------------------------------------------------------ *)
(* the type 'a ** 'b is a cpo *)
(* ------------------------------------------------------------------------ *)
-qed_goal "lub_sprod" Sprod2.thy
+val prems = goal Sprod2.thy
"[|chain(S)|] ==> range(S) <<| \
-\ Ispair (lub(range(%i. Isfst(S i)))) (lub(range(%i. Issnd(S i))))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac (conjI RS is_lubI) 1),
- (rtac (allI RS ub_rangeI) 1),
- (res_inst_tac [("t","S(i)")] (surjective_pairing_Sprod RS ssubst) 1),
- (rtac monofun_Ispair 1),
- (rtac is_ub_thelub 1),
- (etac (monofun_Isfst RS ch2ch_monofun) 1),
- (rtac is_ub_thelub 1),
- (etac (monofun_Issnd RS ch2ch_monofun) 1),
- (strip_tac 1),
- (res_inst_tac [("t","u")] (surjective_pairing_Sprod RS ssubst) 1),
- (rtac monofun_Ispair 1),
- (rtac is_lub_thelub 1),
- (etac (monofun_Isfst RS ch2ch_monofun) 1),
- (etac (monofun_Isfst RS ub2ub_monofun) 1),
- (rtac is_lub_thelub 1),
- (etac (monofun_Issnd RS ch2ch_monofun) 1),
- (etac (monofun_Issnd RS ub2ub_monofun) 1)
- ]);
+\ Ispair (lub(range(%i. Isfst(S i)))) (lub(range(%i. Issnd(S i))))";
+by (cut_facts_tac prems 1);
+by (rtac (conjI RS is_lubI) 1);
+by (rtac (allI RS ub_rangeI) 1);
+by (res_inst_tac [("t","S(i)")] (surjective_pairing_Sprod RS ssubst) 1);
+by (rtac monofun_Ispair 1);
+by (rtac is_ub_thelub 1);
+by (etac (monofun_Isfst RS ch2ch_monofun) 1);
+by (rtac is_ub_thelub 1);
+by (etac (monofun_Issnd RS ch2ch_monofun) 1);
+by (strip_tac 1);
+by (res_inst_tac [("t","u")] (surjective_pairing_Sprod RS ssubst) 1);
+by (rtac monofun_Ispair 1);
+by (rtac is_lub_thelub 1);
+by (etac (monofun_Isfst RS ch2ch_monofun) 1);
+by (etac (monofun_Isfst RS ub2ub_monofun) 1);
+by (rtac is_lub_thelub 1);
+by (etac (monofun_Issnd RS ch2ch_monofun) 1);
+by (etac (monofun_Issnd RS ub2ub_monofun) 1);
+qed "lub_sprod";
bind_thm ("thelub_sprod", lub_sprod RS thelubI);
-qed_goal "cpo_sprod" Sprod2.thy
- "chain(S::nat=>'a**'b)==>? x. range(S)<<| x"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac exI 1),
- (etac lub_sprod 1)
- ]);
-
-
-
-
-
-
-
-
+val prems = goal Sprod2.thy
+ "chain(S::nat=>'a**'b)==>? x. range(S)<<| x";
+by (cut_facts_tac prems 1);
+by (rtac exI 1);
+by (etac lub_sprod 1);
+qed "cpo_sprod";