--- a/src/HOLCF/Lift2.ML Fri Nov 29 12:17:30 1996 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,183 +0,0 @@
-(* Title: HOLCF/lift2.ML
- ID: $Id$
- Author: Franz Regensburger
- Copyright 1993 Technische Universitaet Muenchen
-
-Lemmas for lift2.thy
-*)
-
-open Lift2;
-
-(* -------------------------------------------------------------------------*)
-(* type ('a)u is pointed *)
-(* ------------------------------------------------------------------------ *)
-
-qed_goal "minimal_lift" Lift2.thy "UU_lift << z"
- (fn prems =>
- [
- (stac inst_lift_po 1),
- (rtac less_lift1a 1)
- ]);
-
-(* -------------------------------------------------------------------------*)
-(* access to less_lift in class po *)
-(* ------------------------------------------------------------------------ *)
-
-qed_goal "less_lift2b" Lift2.thy "~ Iup(x) << UU_lift"
- (fn prems =>
- [
- (stac inst_lift_po 1),
- (rtac less_lift1b 1)
- ]);
-
-qed_goal "less_lift2c" Lift2.thy "(Iup(x)<<Iup(y)) = (x<<y)"
- (fn prems =>
- [
- (stac inst_lift_po 1),
- (rtac less_lift1c 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* Iup and Ilift are monotone *)
-(* ------------------------------------------------------------------------ *)
-
-qed_goalw "monofun_Iup" Lift2.thy [monofun] "monofun(Iup)"
- (fn prems =>
- [
- (strip_tac 1),
- (etac (less_lift2c RS iffD2) 1)
- ]);
-
-qed_goalw "monofun_Ilift1" Lift2.thy [monofun] "monofun(Ilift)"
- (fn prems =>
- [
- (strip_tac 1),
- (rtac (less_fun RS iffD2) 1),
- (strip_tac 1),
- (res_inst_tac [("p","xa")] liftE 1),
- (asm_simp_tac Lift0_ss 1),
- (asm_simp_tac Lift0_ss 1),
- (etac monofun_cfun_fun 1)
- ]);
-
-qed_goalw "monofun_Ilift2" Lift2.thy [monofun] "monofun(Ilift(f))"
- (fn prems =>
- [
- (strip_tac 1),
- (res_inst_tac [("p","x")] liftE 1),
- (asm_simp_tac Lift0_ss 1),
- (asm_simp_tac Lift0_ss 1),
- (res_inst_tac [("p","y")] liftE 1),
- (hyp_subst_tac 1),
- (rtac notE 1),
- (rtac less_lift2b 1),
- (atac 1),
- (asm_simp_tac Lift0_ss 1),
- (rtac monofun_cfun_arg 1),
- (hyp_subst_tac 1),
- (etac (less_lift2c RS iffD1) 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* Some kind of surjectivity lemma *)
-(* ------------------------------------------------------------------------ *)
-
-
-qed_goal "lift_lemma1" Lift2.thy "z=Iup(x) ==> Iup(Ilift(LAM x.x)(z)) = z"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (asm_simp_tac Lift0_ss 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* ('a)u is a cpo *)
-(* ------------------------------------------------------------------------ *)
-
-qed_goal "lub_lift1a" Lift2.thy
-"[|is_chain(Y);? i x.Y(i)=Iup(x)|] ==>\
-\ range(Y) <<| Iup(lub(range(%i.(Ilift (LAM x.x) (Y(i))))))"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac is_lubI 1),
- (rtac conjI 1),
- (rtac ub_rangeI 1),
- (rtac allI 1),
- (res_inst_tac [("p","Y(i)")] liftE 1),
- (res_inst_tac [("s","UU_lift"),("t","Y(i)")] subst 1),
- (etac sym 1),
- (rtac minimal_lift 1),
- (res_inst_tac [("t","Y(i)")] (lift_lemma1 RS subst) 1),
- (atac 1),
- (rtac (less_lift2c RS iffD2) 1),
- (rtac is_ub_thelub 1),
- (etac (monofun_Ilift2 RS ch2ch_monofun) 1),
- (strip_tac 1),
- (res_inst_tac [("p","u")] liftE 1),
- (etac exE 1),
- (etac exE 1),
- (res_inst_tac [("P","Y(i)<<UU_lift")] notE 1),
- (res_inst_tac [("s","Iup(x)"),("t","Y(i)")] ssubst 1),
- (atac 1),
- (rtac less_lift2b 1),
- (hyp_subst_tac 1),
- (etac (ub_rangeE RS spec) 1),
- (res_inst_tac [("t","u")] (lift_lemma1 RS subst) 1),
- (atac 1),
- (rtac (less_lift2c RS iffD2) 1),
- (rtac is_lub_thelub 1),
- (etac (monofun_Ilift2 RS ch2ch_monofun) 1),
- (etac (monofun_Ilift2 RS ub2ub_monofun) 1)
- ]);
-
-qed_goal "lub_lift1b" Lift2.thy
-"[|is_chain(Y);!i x. Y(i)~=Iup(x)|] ==>\
-\ range(Y) <<| UU_lift"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac is_lubI 1),
- (rtac conjI 1),
- (rtac ub_rangeI 1),
- (rtac allI 1),
- (res_inst_tac [("p","Y(i)")] liftE 1),
- (res_inst_tac [("s","UU_lift"),("t","Y(i)")] ssubst 1),
- (atac 1),
- (rtac refl_less 1),
- (rtac notE 1),
- (dtac spec 1),
- (dtac spec 1),
- (atac 1),
- (atac 1),
- (strip_tac 1),
- (rtac minimal_lift 1)
- ]);
-
-bind_thm ("thelub_lift1a", lub_lift1a RS thelubI);
-(*
-[| is_chain ?Y1; ? i x. ?Y1 i = Iup x |] ==>
- lub (range ?Y1) = Iup (lub (range (%i. Ilift (LAM x. x) (?Y1 i))))
-*)
-
-bind_thm ("thelub_lift1b", lub_lift1b RS thelubI);
-(*
-[| is_chain ?Y1; ! i x. ?Y1 i ~= Iup x |] ==>
- lub (range ?Y1) = UU_lift
-*)
-
-qed_goal "cpo_lift" Lift2.thy
- "is_chain(Y::nat=>('a)u) ==> ? x.range(Y) <<|x"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac disjE 1),
- (rtac exI 2),
- (etac lub_lift1a 2),
- (atac 2),
- (rtac exI 2),
- (etac lub_lift1b 2),
- (atac 2),
- (fast_tac HOL_cs 1)
- ]);
-