--- a/src/HOLCF/Fix.ML Fri Oct 10 18:37:49 1997 +0200
+++ b/src/HOLCF/Fix.ML Fri Oct 10 19:02:28 1997 +0200
@@ -43,7 +43,7 @@
(* ------------------------------------------------------------------------ *)
qed_goalw "is_chain_iterate2" thy [is_chain]
- " x << F`x ==> is_chain (%i.iterate i F x)"
+ " x << F`x ==> is_chain (%i. iterate i F x)"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -57,7 +57,7 @@
qed_goal "is_chain_iterate" thy
- "is_chain (%i.iterate i F UU)"
+ "is_chain (%i. iterate i F UU)"
(fn prems =>
[
(rtac is_chain_iterate2 1),
@@ -452,16 +452,16 @@
(* ------------------------------------------------------------------------ *)
qed_goalw "admI" thy [adm_def]
- "(!!Y. [| is_chain(Y); !i.P(Y(i)) |] ==> P(lub(range(Y)))) ==> adm(P)"
+ "(!!Y. [| is_chain(Y); !i. P(Y(i)) |] ==> P(lub(range(Y)))) ==> adm(P)"
(fn prems => [fast_tac (HOL_cs addIs prems) 1]);
qed_goalw "admD" thy [adm_def]
- "!!P. [| adm(P); is_chain(Y); !i.P(Y(i)) |] ==> P(lub(range(Y)))"
+ "!!P. [| adm(P); is_chain(Y); !i. P(Y(i)) |] ==> P(lub(range(Y)))"
(fn prems => [fast_tac HOL_cs 1]);
qed_goalw "admw_def2" thy [admw_def]
- "admw(P) = (!F.(!n.P(iterate n F UU)) -->\
-\ P (lub(range(%i.iterate i F UU))))"
+ "admw(P) = (!F.(!n. P(iterate n F UU)) -->\
+\ P (lub(range(%i. iterate i F UU))))"
(fn prems =>
[
(rtac refl 1)
@@ -537,7 +537,7 @@
(* ------------------------------------------------------------------------ *)
qed_goalw "adm_max_in_chain" thy [adm_def]
-"!Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain n Y) ==> adm(P::'a=>bool)"
+"!Y. is_chain(Y::nat=>'a) --> (? n. max_in_chain n Y) ==> adm(P::'a=>bool)"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -585,7 +585,7 @@
(* ------------------------------------------------------------------------ *)
qed_goalw "adm_less" thy [adm_def]
- "[|cont u;cont v|]==> adm(%x.u x << v x)"
+ "[|cont u;cont v|]==> adm(%x. u x << v x)"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -610,7 +610,7 @@
(fn prems => [fast_tac (HOL_cs addEs [admD] addIs [admI]) 1]);
Addsimps [adm_conj];
-qed_goalw "adm_not_free" thy [adm_def] "adm(%x.t)"
+qed_goalw "adm_not_free" thy [adm_def] "adm(%x. t)"
(fn prems => [fast_tac HOL_cs 1]);
Addsimps [adm_not_free];
@@ -629,7 +629,7 @@
]);
qed_goal "adm_all" thy
- "!!P. !y.adm(P y) ==> adm(%x.!y.P y x)"
+ "!!P. !y. adm(P y) ==> adm(%x.!y. P y x)"
(fn prems => [fast_tac (HOL_cs addIs [admI] addEs [admD]) 1]);
bind_thm ("adm_all2", allI RS adm_all);
@@ -681,7 +681,7 @@
local
val adm_disj_lemma1 = prove_goal HOL.thy
- "!n.P(Y n)|Q(Y n) ==> (? i.!j.R i j --> Q(Y(j))) | (!i.? j.R i j & P(Y(j)))"
+ "!n. P(Y n)|Q(Y n) ==> (? i.!j. R i j --> Q(Y(j))) | (!i.? j. R i j & P(Y(j)))"
(fn prems =>
[
(cut_facts_tac prems 1),
@@ -689,7 +689,7 @@
]);
val adm_disj_lemma2 = prove_goal thy
- "!!Q. [| adm(Q); ? X.is_chain(X) & (!n.Q(X(n))) &\
+ "!!Q. [| adm(Q); ? X. is_chain(X) & (!n. Q(X(n))) &\
\ lub(range(Y))=lub(range(X))|] ==> Q(lub(range(Y)))"
(fn _ => [fast_tac (!claset addEs [admD] addss !simpset) 1]);
@@ -735,7 +735,7 @@
[
(cut_facts_tac prems 1),
(etac exE 1),
- (res_inst_tac [("x","%m.if m<Suc(i) then Y(Suc(i)) else Y m")] exI 1),
+ (res_inst_tac [("x","%m. if m<Suc(i) then Y(Suc(i)) else Y m")] exI 1),
(rtac conjI 1),
(rtac adm_disj_lemma3 1),
(atac 1),
@@ -854,7 +854,7 @@
]);
val adm_disj = prove_goal thy
- "!!P. [| adm P; adm Q |] ==> adm(%x.P x | Q x)"
+ "!!P. [| adm P; adm Q |] ==> adm(%x. P x | Q x)"
(fn prems =>
[
(rtac admI 1),
@@ -876,10 +876,10 @@
bind_thm("adm_disj",adm_disj);
qed_goal "adm_imp" thy
- "!!P. [| adm(%x.~(P x)); adm Q |] ==> adm(%x.P x --> Q x)"
+ "!!P. [| adm(%x.~(P x)); adm Q |] ==> adm(%x. P x --> Q x)"
(fn prems =>
[
- (subgoal_tac "(%x.P x --> Q x) = (%x. ~P x | Q x)" 1),
+ (subgoal_tac "(%x. P x --> Q x) = (%x. ~P x | Q x)" 1),
(Asm_simp_tac 1),
(etac adm_disj 1),
(atac 1),
@@ -887,9 +887,9 @@
(fast_tac HOL_cs 1)
]);
-goal Fix.thy "!! P. [| adm (%x. P x --> Q x); adm (%x.Q x --> P x) |] \
+goal Fix.thy "!! P. [| adm (%x. P x --> Q x); adm (%x. Q x --> P x) |] \
\ ==> adm (%x. P x = Q x)";
-by(subgoal_tac "(%x.P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))" 1);
+by(subgoal_tac "(%x. P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))" 1);
by (Asm_simp_tac 1);
by (rtac ext 1);
by (fast_tac HOL_cs 1);