Prod.ML

--- a/Prod.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/Prod.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -11,52 +11,52 @@
 (*This counts as a non-emptiness result for admitting 'a * 'b as a type*)
 goalw Prod.thy [Prod_def] "Pair_Rep(a,b) : Prod";
 by (EVERY1 [rtac CollectI, rtac exI, rtac exI, rtac refl]);
-val ProdI = result();
+qed "ProdI";
 
 val [major] = goalw Prod.thy [Pair_Rep_def]
     "Pair_Rep(a, b) = Pair_Rep(a',b') ==> a=a' & b=b'";
 by (EVERY1 [rtac (major RS fun_cong RS fun_cong RS subst), 
 	    rtac conjI, rtac refl, rtac refl]);
-val Pair_Rep_inject = result();
+qed "Pair_Rep_inject";
 
 goal Prod.thy "inj_onto(Abs_Prod,Prod)";
 by (rtac inj_onto_inverseI 1);
 by (etac Abs_Prod_inverse 1);
-val inj_onto_Abs_Prod = result();
+qed "inj_onto_Abs_Prod";
 
 val prems = goalw Prod.thy [Pair_def]
     "[| <a, b> = <a',b'>;  [| a=a';  b=b' |] ==> R |] ==> R";
 by (rtac (inj_onto_Abs_Prod RS inj_ontoD RS Pair_Rep_inject RS conjE) 1);
 by (REPEAT (ares_tac (prems@[ProdI]) 1));
-val Pair_inject = result();
+qed "Pair_inject";
 
 goal Prod.thy "(<a,b> = <a',b'>) = (a=a' & b=b')";
 by (fast_tac (set_cs addIs [Pair_inject]) 1);
-val Pair_eq = result();
+qed "Pair_eq";
 
 goalw Prod.thy [fst_def] "fst(<a,b>) = a";
 by (fast_tac (set_cs addIs [select_equality] addSEs [Pair_inject]) 1);
-val fst_conv = result();
+qed "fst_conv";
 
 goalw Prod.thy [snd_def] "snd(<a,b>) = b";
 by (fast_tac (set_cs addIs [select_equality] addSEs [Pair_inject]) 1);
-val snd_conv = result();
+qed "snd_conv";
 
 goalw Prod.thy [Pair_def] "? x y. p = <x,y>";
 by (rtac (rewrite_rule [Prod_def] Rep_Prod RS CollectE) 1);
 by (EVERY1[etac exE, etac exE, rtac exI, rtac exI,
 	   rtac (Rep_Prod_inverse RS sym RS trans),  etac arg_cong]);
-val PairE_lemma = result();
+qed "PairE_lemma";
 
 val [prem] = goal Prod.thy "[| !!x y. p = <x,y> ==> Q |] ==> Q";
 by (rtac (PairE_lemma RS exE) 1);
 by (REPEAT (eresolve_tac [prem,exE] 1));
-val PairE = result();
+qed "PairE";
 
 goalw Prod.thy [split_def] "split(c, <a,b>) = c(a,b)";
 by (sstac [fst_conv, snd_conv] 1);
 by (rtac refl 1);
-val split = result();
+qed "split";
 
 val pair_ss = set_ss addsimps [fst_conv, snd_conv, split, Pair_eq];
 
@@ -64,7 +64,7 @@
 by (res_inst_tac[("p","s")] PairE 1);
 by (res_inst_tac[("p","t")] PairE 1);
 by (asm_simp_tac pair_ss 1);
-val Pair_fst_snd_eq = result();
+qed "Pair_fst_snd_eq";
 
 (*Prevents simplification of c: much faster*)
 val split_weak_cong = prove_goal Prod.thy
@@ -74,19 +74,19 @@
 goal Prod.thy "p = <fst(p),snd(p)>";
 by (res_inst_tac [("p","p")] PairE 1);
 by (asm_simp_tac pair_ss 1);
-val surjective_pairing = result();
+qed "surjective_pairing";
 
 goal Prod.thy "p = split(%x y.<x,y>, p)";
 by (res_inst_tac [("p","p")] PairE 1);
 by (asm_simp_tac pair_ss 1);
-val surjective_pairing2 = result();
+qed "surjective_pairing2";
 
 (*For use with split_tac and the simplifier*)
 goal Prod.thy "R(split(c,p)) = (! x y. p = <x,y> --> R(c(x,y)))";
 by (stac surjective_pairing 1);
 by (stac split 1);
 by (fast_tac (HOL_cs addSEs [Pair_inject]) 1);
-val expand_split = result();
+qed "expand_split";
 
 (** split used as a logical connective or set former **)
 
@@ -95,50 +95,50 @@
 
 goal Prod.thy "!!a b c. c(a,b) ==> split(c, <a,b>)";
 by (asm_simp_tac pair_ss 1);
-val splitI = result();
+qed "splitI";
 
 val prems = goalw Prod.thy [split_def]
     "[| split(c,p);  !!x y. [| p = <x,y>;  c(x,y) |] ==> Q |] ==> Q";
 by (REPEAT (resolve_tac (prems@[surjective_pairing]) 1));
-val splitE = result();
+qed "splitE";
 
 goal Prod.thy "!!R a b. split(R,<a,b>) ==> R(a,b)";
 by (etac (split RS iffD1) 1);
-val splitD = result();
+qed "splitD";
 
 goal Prod.thy "!!a b c. z: c(a,b) ==> z: split(c, <a,b>)";
 by (asm_simp_tac pair_ss 1);
-val mem_splitI = result();
+qed "mem_splitI";
 
 val prems = goalw Prod.thy [split_def]
     "[| z: split(c,p);  !!x y. [| p = <x,y>;  z: c(x,y) |] ==> Q |] ==> Q";
 by (REPEAT (resolve_tac (prems@[surjective_pairing]) 1));
-val mem_splitE = result();
+qed "mem_splitE";
 
 (*** prod_fun -- action of the product functor upon functions ***)
 
 goalw Prod.thy [prod_fun_def] "prod_fun(f,g,<a,b>) = <f(a),g(b)>";
 by (rtac split 1);
-val prod_fun = result();
+qed "prod_fun";
 
 goal Prod.thy 
     "prod_fun(f1 o f2, g1 o g2) = (prod_fun(f1,g1) o prod_fun(f2,g2))";
 by (rtac ext 1);
 by (res_inst_tac [("p","x")] PairE 1);
 by (asm_simp_tac (pair_ss addsimps [prod_fun,o_def]) 1);
-val prod_fun_compose = result();
+qed "prod_fun_compose";
 
 goal Prod.thy "prod_fun(%x.x, %y.y) = (%z.z)";
 by (rtac ext 1);
 by (res_inst_tac [("p","z")] PairE 1);
 by (asm_simp_tac (pair_ss addsimps [prod_fun]) 1);
-val prod_fun_ident = result();
+qed "prod_fun_ident";
 
 val prems = goal Prod.thy "<a,b>:r ==> <f(a),g(b)> : prod_fun(f,g)``r";
 by (rtac image_eqI 1);
 by (rtac (prod_fun RS sym) 1);
 by (resolve_tac prems 1);
-val prod_fun_imageI = result();
+qed "prod_fun_imageI";
 
 val major::prems = goal Prod.thy
     "[| c: prod_fun(f,g)``r;  !!x y. [| c=<f(x),g(y)>;  <x,y>:r |] ==> P  \
@@ -148,7 +148,7 @@
 by (resolve_tac prems 1);
 by (fast_tac HOL_cs 2);
 by (fast_tac (HOL_cs addIs [prod_fun]) 1);
-val prod_fun_imageE = result();
+qed "prod_fun_imageE";
 
 (*** Disjoint union of a family of sets - Sigma ***)
 
@@ -192,7 +192,7 @@
 by (rtac bexI 1);
 by (rtac (fst_conv RS sym) 1);
 by (resolve_tac prems 1);
-val fst_imageI = result();
+qed "fst_imageI";
 
 val major::prems = goal Prod.thy
     "[| a : fst``r;  !!y.[| <a,y> : r |] ==> P |] ==> P"; 
@@ -201,7 +201,7 @@
 by (etac ssubst 1);
 by (rtac (surjective_pairing RS subst) 1);
 by (assume_tac 1);
-val fst_imageE = result();
+qed "fst_imageE";
 
 (*** Range of a relation ***)
 
@@ -210,7 +210,7 @@
 by (rtac bexI 1);
 by (rtac (snd_conv RS sym) 1);
 by (resolve_tac prems 1);
-val snd_imageI = result();
+qed "snd_imageI";
 
 val major::prems = goal Prod.thy
     "[| a : snd``r;  !!y.[| <y,a> : r |] ==> P |] ==> P"; 
@@ -219,7 +219,7 @@
 by (etac ssubst 1);
 by (rtac (surjective_pairing RS subst) 1);
 by (assume_tac 1);
-val snd_imageE = result();
+qed "snd_imageE";
 
 (** Exhaustion rule for unit -- a degenerate form of induction **)
 
@@ -227,7 +227,7 @@
     "u = Unity";
 by (stac (rewrite_rule [Unit_def] Rep_Unit RS CollectD RS sym) 1);
 by (rtac (Rep_Unit_inverse RS sym) 1);
-val unit_eq = result();
+qed "unit_eq";
 
 val prod_cs = set_cs addSIs [SigmaI, mem_splitI] 
                      addIs  [fst_imageI, snd_imageI, prod_fun_imageI]