--- a/src/ZF/pair.ML Wed Apr 02 15:37:35 1997 +0200
+++ b/src/ZF/pair.ML Wed Apr 02 15:39:44 1997 +0200
@@ -8,20 +8,20 @@
(** Lemmas for showing that <a,b> uniquely determines a and b **)
-qed_goal "singleton_eq_iff" thy
+qed_goal "singleton_eq_iff" ZF.thy
"{a} = {b} <-> a=b"
(fn _=> [ (resolve_tac [extension RS iff_trans] 1),
- (Fast_tac 1) ]);
+ (Blast_tac 1) ]);
-qed_goal "doubleton_eq_iff" thy
+qed_goal "doubleton_eq_iff" ZF.thy
"{a,b} = {c,d} <-> (a=c & b=d) | (a=d & b=c)"
(fn _=> [ (resolve_tac [extension RS iff_trans] 1),
- (Fast_tac 1) ]);
+ (Blast_tac 1) ]);
-qed_goalw "Pair_iff" thy [Pair_def]
+qed_goalw "Pair_iff" ZF.thy [Pair_def]
"<a,b> = <c,d> <-> a=c & b=d"
(fn _=> [ (simp_tac (!simpset addsimps [doubleton_eq_iff]) 1),
- (Fast_tac 1) ]);
+ (Blast_tac 1) ]);
Addsimps [Pair_iff];
@@ -32,20 +32,20 @@
bind_thm ("Pair_inject1", Pair_iff RS iffD1 RS conjunct1);
bind_thm ("Pair_inject2", Pair_iff RS iffD1 RS conjunct2);
-qed_goalw "Pair_not_0" thy [Pair_def] "<a,b> ~= 0"
- (fn _ => [ (fast_tac (!claset addEs [equalityE]) 1) ]);
+qed_goalw "Pair_not_0" ZF.thy [Pair_def] "<a,b> ~= 0"
+ (fn _ => [ (blast_tac (!claset addEs [equalityE]) 1) ]);
bind_thm ("Pair_neq_0", Pair_not_0 RS notE);
AddSEs [Pair_neq_0, sym RS Pair_neq_0];
-qed_goalw "Pair_neq_fst" thy [Pair_def] "<a,b>=a ==> P"
+qed_goalw "Pair_neq_fst" ZF.thy [Pair_def] "<a,b>=a ==> P"
(fn [major]=>
[ (rtac (consI1 RS mem_asym RS FalseE) 1),
(rtac (major RS subst) 1),
(rtac consI1 1) ]);
-qed_goalw "Pair_neq_snd" thy [Pair_def] "<a,b>=b ==> P"
+qed_goalw "Pair_neq_snd" ZF.thy [Pair_def] "<a,b>=b ==> P"
(fn [major]=>
[ (rtac (consI1 RS consI2 RS mem_asym RS FalseE) 1),
(rtac (major RS subst) 1),
@@ -55,12 +55,12 @@
(*** Sigma: Disjoint union of a family of sets
Generalizes Cartesian product ***)
-qed_goalw "Sigma_iff" thy [Sigma_def] "<a,b>: Sigma(A,B) <-> a:A & b:B(a)"
- (fn _ => [ Fast_tac 1 ]);
+qed_goalw "Sigma_iff" ZF.thy [Sigma_def] "<a,b>: Sigma(A,B) <-> a:A & b:B(a)"
+ (fn _ => [ Blast_tac 1 ]);
Addsimps [Sigma_iff];
-qed_goal "SigmaI" thy
+qed_goal "SigmaI" ZF.thy
"!!a b. [| a:A; b:B(a) |] ==> <a,b> : Sigma(A,B)"
(fn _ => [ Asm_simp_tac 1 ]);
@@ -68,7 +68,7 @@
bind_thm ("SigmaD2", Sigma_iff RS iffD1 RS conjunct2);
(*The general elimination rule*)
-qed_goalw "SigmaE" thy [Sigma_def]
+qed_goalw "SigmaE" ZF.thy [Sigma_def]
"[| c: Sigma(A,B); \
\ !!x y.[| x:A; y:B(x); c=<x,y> |] ==> P \
\ |] ==> P"
@@ -76,7 +76,7 @@
[ (cut_facts_tac [major] 1),
(REPEAT (eresolve_tac [UN_E, singletonE] 1 ORELSE ares_tac prems 1)) ]);
-qed_goal "SigmaE2" thy
+qed_goal "SigmaE2" ZF.thy
"[| <a,b> : Sigma(A,B); \
\ [| a:A; b:B(a) |] ==> P \
\ |] ==> P"
@@ -85,7 +85,7 @@
(rtac (major RS SigmaD1) 1),
(rtac (major RS SigmaD2) 1) ]);
-qed_goalw "Sigma_cong" thy [Sigma_def]
+qed_goalw "Sigma_cong" ZF.thy [Sigma_def]
"[| A=A'; !!x. x:A' ==> B(x)=B'(x) |] ==> \
\ Sigma(A,B) = Sigma(A',B')"
(fn prems=> [ (simp_tac (!simpset addsimps prems) 1) ]);
@@ -98,32 +98,32 @@
AddSIs [SigmaI];
AddSEs [SigmaE2, SigmaE];
-qed_goal "Sigma_empty1" thy "Sigma(0,B) = 0"
- (fn _ => [ (Fast_tac 1) ]);
+qed_goal "Sigma_empty1" ZF.thy "Sigma(0,B) = 0"
+ (fn _ => [ (Blast_tac 1) ]);
-qed_goal "Sigma_empty2" thy "A*0 = 0"
- (fn _ => [ (Fast_tac 1) ]);
+qed_goal "Sigma_empty2" ZF.thy "A*0 = 0"
+ (fn _ => [ (Blast_tac 1) ]);
Addsimps [Sigma_empty1, Sigma_empty2];
(*** Projections: fst, snd ***)
-qed_goalw "fst_conv" thy [fst_def] "fst(<a,b>) = a"
- (fn _=> [ (fast_tac (!claset addIs [the_equality]) 1) ]);
+qed_goalw "fst_conv" ZF.thy [fst_def] "fst(<a,b>) = a"
+ (fn _=> [ (blast_tac (!claset addIs [the_equality]) 1) ]);
-qed_goalw "snd_conv" thy [snd_def] "snd(<a,b>) = b"
- (fn _=> [ (fast_tac (!claset addIs [the_equality]) 1) ]);
+qed_goalw "snd_conv" ZF.thy [snd_def] "snd(<a,b>) = b"
+ (fn _=> [ (blast_tac (!claset addIs [the_equality]) 1) ]);
Addsimps [fst_conv,snd_conv];
-qed_goal "fst_type" thy "!!p. p:Sigma(A,B) ==> fst(p) : A"
+qed_goal "fst_type" ZF.thy "!!p. p:Sigma(A,B) ==> fst(p) : A"
(fn _=> [ Auto_tac() ]);
-qed_goal "snd_type" thy "!!p. p:Sigma(A,B) ==> snd(p) : B(fst(p))"
+qed_goal "snd_type" ZF.thy "!!p. p:Sigma(A,B) ==> snd(p) : B(fst(p))"
(fn _=> [ Auto_tac() ]);
-qed_goal "Pair_fst_snd_eq" thy
+qed_goal "Pair_fst_snd_eq" ZF.thy
"!!a A B. a: Sigma(A,B) ==> <fst(a),snd(a)> = a"
(fn _=> [ Auto_tac() ]);
@@ -131,13 +131,13 @@
(*** Eliminator - split ***)
(*A META-equality, so that it applies to higher types as well...*)
-qed_goalw "split" thy [split_def] "split(%x y.c(x,y), <a,b>) == c(a,b)"
+qed_goalw "split" ZF.thy [split_def] "split(%x y.c(x,y), <a,b>) == c(a,b)"
(fn _ => [ (Simp_tac 1),
(rtac reflexive_thm 1) ]);
Addsimps [split];
-qed_goal "split_type" thy
+qed_goal "split_type" ZF.thy
"[| p:Sigma(A,B); \
\ !!x y.[| x:A; y:B(x) |] ==> c(x,y):C(<x,y>) \
\ |] ==> split(%x y.c(x,y), p) : C(p)"
@@ -145,7 +145,7 @@
[ (rtac (major RS SigmaE) 1),
(asm_simp_tac (!simpset addsimps prems) 1) ]);
-goalw thy [split_def]
+goalw ZF.thy [split_def]
"!!u. u: A*B ==> \
\ R(split(c,u)) <-> (ALL x:A. ALL y:B. u = <x,y> --> R(c(x,y)))";
by (Auto_tac());
@@ -154,11 +154,11 @@
(*** split for predicates: result type o ***)
-goalw thy [split_def] "!!R a b. R(a,b) ==> split(R, <a,b>)";
+goalw ZF.thy [split_def] "!!R a b. R(a,b) ==> split(R, <a,b>)";
by (Asm_simp_tac 1);
qed "splitI";
-val major::sigma::prems = goalw thy [split_def]
+val major::sigma::prems = goalw ZF.thy [split_def]
"[| split(R,z); z:Sigma(A,B); \
\ !!x y. [| z = <x,y>; R(x,y) |] ==> P \
\ |] ==> P";
@@ -168,7 +168,7 @@
by (Asm_full_simp_tac 1);
qed "splitE";
-goalw thy [split_def] "!!R a b. split(R,<a,b>) ==> R(a,b)";
+goalw ZF.thy [split_def] "!!R a b. split(R,<a,b>) ==> R(a,b)";
by (Full_simp_tac 1);
qed "splitD";