--- a/src/HOLCF/pcpo.ML Sat Apr 05 17:03:38 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,272 +0,0 @@
-(* Title: HOLCF/pcpo.ML
- ID: $Id$
- Author: Franz Regensburger
- Copyright 1993 Technische Universitaet Muenchen
-
-Lemmas for pcpo.thy
-*)
-
-open Pcpo;
-
-(* ------------------------------------------------------------------------ *)
-(* in pcpo's everthing equal to THE lub has lub properties for every chain *)
-(* ------------------------------------------------------------------------ *)
-
-val thelubE = prove_goal Pcpo.thy
- "[| is_chain(S);lub(range(S)) = l::'a::pcpo|] ==> range(S) <<| l "
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (hyp_subst_tac 1),
- (rtac lubI 1),
- (etac cpo 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* Properties of the lub *)
-(* ------------------------------------------------------------------------ *)
-
-
-val is_ub_thelub = (cpo RS lubI RS is_ub_lub);
-(* is_chain(?S1) ==> ?S1(?x) << lub(range(?S1)) *)
-
-val is_lub_thelub = (cpo RS lubI RS is_lub_lub);
-(* [| is_chain(?S5); range(?S5) <| ?x1 |] ==> lub(range(?S5)) << ?x1 *)
-
-
-(* ------------------------------------------------------------------------ *)
-(* the << relation between two chains is preserved by their lubs *)
-(* ------------------------------------------------------------------------ *)
-
-val lub_mono = prove_goal Pcpo.thy
- "[|is_chain(C1::(nat=>'a::pcpo));is_chain(C2); ! k. C1(k) << C2(k)|]\
-\ ==> lub(range(C1)) << lub(range(C2))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (etac is_lub_thelub 1),
- (rtac ub_rangeI 1),
- (rtac allI 1),
- (rtac trans_less 1),
- (etac spec 1),
- (etac is_ub_thelub 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* the = relation between two chains is preserved by their lubs *)
-(* ------------------------------------------------------------------------ *)
-
-val lub_equal = prove_goal Pcpo.thy
-"[| is_chain(C1::(nat=>'a::pcpo));is_chain(C2);!k.C1(k)=C2(k)|]\
-\ ==> lub(range(C1))=lub(range(C2))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac antisym_less 1),
- (rtac lub_mono 1),
- (atac 1),
- (atac 1),
- (strip_tac 1),
- (rtac (antisym_less_inverse RS conjunct1) 1),
- (etac spec 1),
- (rtac lub_mono 1),
- (atac 1),
- (atac 1),
- (strip_tac 1),
- (rtac (antisym_less_inverse RS conjunct2) 1),
- (etac spec 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* more results about mono and = of lubs of chains *)
-(* ------------------------------------------------------------------------ *)
-
-val lub_mono2 = prove_goal Pcpo.thy
-"[|? j.!i. j<i --> X(i::nat)=Y(i);is_chain(X::nat=>'a::pcpo);is_chain(Y)|]\
-\ ==> lub(range(X))<<lub(range(Y))"
- (fn prems =>
- [
- (rtac exE 1),
- (resolve_tac prems 1),
- (rtac is_lub_thelub 1),
- (resolve_tac prems 1),
- (rtac ub_rangeI 1),
- (strip_tac 1),
- (res_inst_tac [("Q","x<i")] classical2 1),
- (res_inst_tac [("s","Y(i)"),("t","X(i)")] subst 1),
- (rtac sym 1),
- (fast_tac HOL_cs 1),
- (rtac is_ub_thelub 1),
- (resolve_tac prems 1),
- (res_inst_tac [("y","X(Suc(x))")] trans_less 1),
- (rtac (chain_mono RS mp) 1),
- (resolve_tac prems 1),
- (rtac (not_less_eq RS subst) 1),
- (atac 1),
- (res_inst_tac [("s","Y(Suc(x))"),("t","X(Suc(x))")] subst 1),
- (rtac sym 1),
- (asm_simp_tac nat_ss 1),
- (rtac is_ub_thelub 1),
- (resolve_tac prems 1)
- ]);
-
-val lub_equal2 = prove_goal Pcpo.thy
-"[|? j.!i. j<i --> X(i)=Y(i);is_chain(X::nat=>'a::pcpo);is_chain(Y)|]\
-\ ==> lub(range(X))=lub(range(Y))"
- (fn prems =>
- [
- (rtac antisym_less 1),
- (rtac lub_mono2 1),
- (REPEAT (resolve_tac prems 1)),
- (cut_facts_tac prems 1),
- (rtac lub_mono2 1),
- (safe_tac HOL_cs),
- (step_tac HOL_cs 1),
- (safe_tac HOL_cs),
- (rtac sym 1),
- (fast_tac HOL_cs 1)
- ]);
-
-val lub_mono3 = prove_goal Pcpo.thy "[|is_chain(Y::nat=>'a::pcpo);is_chain(X);\
-\! i. ? j. Y(i)<< X(j)|]==> lub(range(Y))<<lub(range(X))"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac is_lub_thelub 1),
- (atac 1),
- (rtac ub_rangeI 1),
- (strip_tac 1),
- (etac allE 1),
- (etac exE 1),
- (rtac trans_less 1),
- (rtac is_ub_thelub 2),
- (atac 2),
- (atac 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* usefull lemmas about UU *)
-(* ------------------------------------------------------------------------ *)
-
-val eq_UU_iff = prove_goal Pcpo.thy "(x=UU)=(x<<UU)"
- (fn prems =>
- [
- (rtac iffI 1),
- (hyp_subst_tac 1),
- (rtac refl_less 1),
- (rtac antisym_less 1),
- (atac 1),
- (rtac minimal 1)
- ]);
-
-val UU_I = prove_goal Pcpo.thy "x << UU ==> x = UU"
- (fn prems =>
- [
- (rtac (eq_UU_iff RS ssubst) 1),
- (resolve_tac prems 1)
- ]);
-
-val not_less2not_eq = prove_goal Pcpo.thy "~x<<y ==> ~x=y"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac classical3 1),
- (atac 1),
- (hyp_subst_tac 1),
- (rtac refl_less 1)
- ]);
-
-
-val chain_UU_I = prove_goal Pcpo.thy
- "[|is_chain(Y);lub(range(Y))=UU|] ==> ! i.Y(i)=UU"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac allI 1),
- (rtac antisym_less 1),
- (rtac minimal 2),
- (res_inst_tac [("t","UU")] subst 1),
- (atac 1),
- (etac is_ub_thelub 1)
- ]);
-
-
-val chain_UU_I_inverse = prove_goal Pcpo.thy
- "!i.Y(i::nat)=UU ==> lub(range(Y::(nat=>'a::pcpo)))=UU"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac lub_chain_maxelem 1),
- (rtac is_chainI 1),
- (rtac allI 1),
- (res_inst_tac [("s","UU"),("t","Y(i)")] subst 1),
- (rtac sym 1),
- (etac spec 1),
- (rtac minimal 1),
- (rtac exI 1),
- (etac spec 1),
- (rtac allI 1),
- (rtac (antisym_less_inverse RS conjunct1) 1),
- (etac spec 1)
- ]);
-
-val chain_UU_I_inverse2 = prove_goal Pcpo.thy
- "~lub(range(Y::(nat=>'a::pcpo)))=UU ==> ? i.~ Y(i)=UU"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac (notall2ex RS iffD1) 1),
- (rtac swap 1),
- (rtac chain_UU_I_inverse 2),
- (etac notnotD 2),
- (atac 1)
- ]);
-
-
-val notUU_I = prove_goal Pcpo.thy "[| x<<y; ~x=UU |] ==> ~y=UU"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (etac contrapos 1),
- (rtac UU_I 1),
- (hyp_subst_tac 1),
- (atac 1)
- ]);
-
-
-val chain_mono2 = prove_goal Pcpo.thy
-"[|? j.~Y(j)=UU;is_chain(Y::nat=>'a::pcpo)|]\
-\ ==> ? j.!i.j<i-->~Y(i)=UU"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (safe_tac HOL_cs),
- (step_tac HOL_cs 1),
- (strip_tac 1),
- (rtac notUU_I 1),
- (atac 2),
- (etac (chain_mono RS mp) 1),
- (atac 1)
- ]);
-
-
-
-
-(* ------------------------------------------------------------------------ *)
-(* uniqueness in void *)
-(* ------------------------------------------------------------------------ *)
-
-val unique_void2 = prove_goal Pcpo.thy "x::void=UU"
- (fn prems =>
- [
- (rtac (inst_void_pcpo RS ssubst) 1),
- (rtac (Rep_Void_inverse RS subst) 1),
- (rtac (Rep_Void_inverse RS subst) 1),
- (rtac arg_cong 1),
- (rtac box_equals 1),
- (rtac refl 1),
- (rtac (unique_void RS sym) 1),
- (rtac (unique_void RS sym) 1)
- ]);
-
-