removed old version of LEAST operator
authoroheimb
Thu, 27 Jun 1996 12:53:08 +0200
changeset 1832 79dd1433867c
parent 1831 fafd8ecbc246
child 1833 59f5256d8dd2
removed old version of LEAST operator
src/HOLCF/Holcfb.ML
src/HOLCF/Holcfb.thy
--- a/src/HOLCF/Holcfb.ML	Wed Jun 26 17:50:10 1996 +0200
+++ b/src/HOLCF/Holcfb.ML	Thu Jun 27 12:53:08 1996 +0200
@@ -9,70 +9,6 @@
 open Holcfb;
 
 (* ------------------------------------------------------------------------ *)
-(* <::nat=>nat=>bool is a well-ordering                                     *)
-(* ------------------------------------------------------------------------ *)
-
-(*
-qed_goal "well_ordering_nat"  Nat.thy 
-        "!P. P(x::nat) --> (? y. P(y) & (! x. P(x) --> y <= x))"
- (fn prems =>
-        [
-        (res_inst_tac [("n","x")] less_induct 1),
-        (strip_tac 1),
-        (res_inst_tac [("Q","? k.k<n & P(k)")] (excluded_middle RS disjE) 1),
-        (etac exE 2),
-        (etac conjE 2),
-        (rtac mp 2),
-        (etac allE 2),
-        (etac impE 2),
-        (atac 2),
-        (etac spec 2),
-        (atac 2),
-        (res_inst_tac [("x","n")] exI 1),
-        (rtac conjI 1),
-        (atac 1),
-        (strip_tac 1),
-        (rtac leI  1),
-        (fast_tac HOL_cs 1)
-        ]);
-*)
-
-(* ------------------------------------------------------------------------ *)
-(* Lemmas for selecting the least element in a nonempty set                 *)
-(* ------------------------------------------------------------------------ *)
-
-(*
-qed_goalw "theleast"  Holcfb.thy [theleast_def] 
-"P(x) ==> P(theleast(P)) & (!x.P(x)--> theleast(P) <= x)"
- (fn prems =>
-        [
-        (cut_facts_tac prems 1),
-        (rtac (well_ordering_nat RS spec RS mp RS exE) 1),
-        (atac 1),
-        (rtac selectI 1),
-        (atac 1)
-        ]);
-*)
-
-
-(* val theleast1 = LeastI "?P ?k  ?P (x. ?P x)" *)
-(*
-val theleast1= theleast RS conjunct1;
-(* ?P1(?x1) ==> ?P1(theleast(?P1)) *)
-*)
-
-(* val theleast2 = Least_le "?P ?k  (x. ?P x) <= ?k" *)
-(*
-qed_goal "theleast2"  Holcfb.thy  "P(x) ==> theleast(P) <= x"
- (fn prems =>
-        [
-        (rtac (theleast RS conjunct2 RS spec RS mp) 1),
-        (resolve_tac prems 1),
-        (resolve_tac prems 1)
-        ]);
-*)
-
-(* ------------------------------------------------------------------------ *)
 (* Some lemmas in HOL.thy                                                   *)
 (* ------------------------------------------------------------------------ *)
 
@@ -102,39 +38,7 @@
 *)
 
 (* val classical2 = case_split_thm;        "[|Q ==> R; ~Q ==> R|]==>R" *)
-(*
-qed_goal "classical2" HOL.thy "[|Q ==> R; ~Q ==> R|]==>R"
- (fn prems =>
-        [
-        (rtac disjE 1),
-        (rtac excluded_middle 1),
-        (eresolve_tac prems 1),
-        (eresolve_tac prems 1)
-        ]);
-*)
-(*
-fun case_tac s = res_inst_tac [("Q",s)] classical2;
-*)
-
-
 
-val classical3 = (notE RS notI);
-(* [| ?P ==> ~ ?P1; ?P ==> ?P1 |] ==> ~ ?P *)
+(* fun case_tac s = res_inst_tac [("Q",s)] classical2; *)
 
-(*
-qed_goal "nat_less_cases" Nat.thy 
-    "[| (m::nat) < n ==> P(n,m); m=n ==> P(n,m);n < m ==> P(n,m)|]==>P(n,m)"
-( fn prems =>
-        [
-        (res_inst_tac [("m1","n"),("n1","m")] (less_linear RS disjE) 1),
-        (etac disjE 2),
-        (etac (hd (tl (tl prems))) 1),
-        (etac (sym RS hd (tl prems)) 1),
-        (etac (hd prems) 1)
-        ]);
-*)
-
-(*
-qed_goal "Suc_less_mono" Nat.thy "Suc n < Suc m = (n < m)" (fn _ => [
-	fast_tac (HOL_cs addIs [Suc_mono] addDs [Suc_less_SucD]) 1]);
-*)
+val classical3 = (notE RS notI); (* [| ?P ==> ~ ?P1; ?P ==> ?P1 |] ==> ~ ?P *)
--- a/src/HOLCF/Holcfb.thy	Wed Jun 26 17:50:10 1996 +0200
+++ b/src/HOLCF/Holcfb.thy	Thu Jun 27 12:53:08 1996 +0200
@@ -8,24 +8,3 @@
 *)
 
 Holcfb = Nat 
-
-(* + 
-
-consts
-        theleast     :: "(nat=>bool)=>nat"
-defs
-
-theleast_def    "theleast P == (@z.(P z & (!n.P n --> z<=n)))"
-
-(* start 8bit 1 *)
-
-syntax
-  "Gmu"        :: "[pttrn, bool] => nat"               ("(3_./ _)" 10)
-
-translations
-  "x.P"	== "theleast(%x.P)"
-
-(* end 8bit 1 *)
-
-end
-*)
\ No newline at end of file