diff -r 02c12d4c8b97 -r 6476784dba1c src/ZF/domrange.ML --- a/src/ZF/domrange.ML Wed Apr 02 15:37:35 1997 +0200 +++ b/src/ZF/domrange.ML Wed Apr 02 15:39:44 1997 +0200 @@ -8,19 +8,19 @@ (*** converse ***) -qed_goalw "converse_iff" thy [converse_def] +qed_goalw "converse_iff" ZF.thy [converse_def] ": converse(r) <-> :r" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "converseI" thy [converse_def] +qed_goalw "converseI" ZF.thy [converse_def] "!!a b r. :r ==> :converse(r)" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "converseD" thy [converse_def] +qed_goalw "converseD" ZF.thy [converse_def] "!!a b r. : converse(r) ==> : r" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "converseE" thy [converse_def] +qed_goalw "converseE" ZF.thy [converse_def] "[| yx : converse(r); \ \ !!x y. [| yx=; :r |] ==> P \ \ |] ==> P" @@ -34,31 +34,31 @@ AddSIs [converseI]; AddSEs [converseD,converseE]; -qed_goal "converse_converse" thy +qed_goal "converse_converse" ZF.thy "!!A B r. r<=Sigma(A,B) ==> converse(converse(r)) = r" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goal "converse_type" thy "!!A B r. r<=A*B ==> converse(r)<=B*A" - (fn _ => [ (Fast_tac 1) ]); +qed_goal "converse_type" ZF.thy "!!A B r. r<=A*B ==> converse(r)<=B*A" + (fn _ => [ (Blast_tac 1) ]); -qed_goal "converse_prod" thy "converse(A*B) = B*A" - (fn _ => [ (Fast_tac 1) ]); +qed_goal "converse_prod" ZF.thy "converse(A*B) = B*A" + (fn _ => [ (Blast_tac 1) ]); -qed_goal "converse_empty" thy "converse(0) = 0" - (fn _ => [ (Fast_tac 1) ]); +qed_goal "converse_empty" ZF.thy "converse(0) = 0" + (fn _ => [ (Blast_tac 1) ]); Addsimps [converse_prod, converse_empty]; (*** domain ***) -qed_goalw "domain_iff" thy [domain_def] +qed_goalw "domain_iff" ZF.thy [domain_def] "a: domain(r) <-> (EX y. : r)" - (fn _=> [ (Fast_tac 1) ]); + (fn _=> [ (Blast_tac 1) ]); -qed_goal "domainI" thy "!!a b r. : r ==> a: domain(r)" +qed_goal "domainI" ZF.thy "!!a b r. : r ==> a: domain(r)" (fn _=> [ (etac (exI RS (domain_iff RS iffD2)) 1) ]); -qed_goal "domainE" thy +qed_goal "domainE" ZF.thy "[| a : domain(r); !!y. : r ==> P |] ==> P" (fn prems=> [ (rtac (domain_iff RS iffD1 RS exE) 1), @@ -67,15 +67,15 @@ AddIs [domainI]; AddSEs [domainE]; -qed_goal "domain_subset" thy "domain(Sigma(A,B)) <= A" - (fn _=> [ (Fast_tac 1) ]); +qed_goal "domain_subset" ZF.thy "domain(Sigma(A,B)) <= A" + (fn _=> [ (Blast_tac 1) ]); (*** range ***) -qed_goalw "rangeI" thy [range_def] "!!a b r.: r ==> b : range(r)" +qed_goalw "rangeI" ZF.thy [range_def] "!!a b r.: r ==> b : range(r)" (fn _ => [ (etac (converseI RS domainI) 1) ]); -qed_goalw "rangeE" thy [range_def] +qed_goalw "rangeE" ZF.thy [range_def] "[| b : range(r); !!x. : r ==> P |] ==> P" (fn major::prems=> [ (rtac (major RS domainE) 1), @@ -85,7 +85,7 @@ AddIs [rangeI]; AddSEs [rangeE]; -qed_goalw "range_subset" thy [range_def] "range(A*B) <= B" +qed_goalw "range_subset" ZF.thy [range_def] "range(A*B) <= B" (fn _ => [ (stac converse_prod 1), (rtac domain_subset 1) ]); @@ -93,17 +93,17 @@ (*** field ***) -qed_goalw "fieldI1" thy [field_def] "!!r. : r ==> a : field(r)" - (fn _ => [ (Fast_tac 1) ]); +qed_goalw "fieldI1" ZF.thy [field_def] "!!r. : r ==> a : field(r)" + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "fieldI2" thy [field_def] "!!r. : r ==> b : field(r)" - (fn _ => [ (Fast_tac 1) ]); +qed_goalw "fieldI2" ZF.thy [field_def] "!!r. : r ==> b : field(r)" + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "fieldCI" thy [field_def] +qed_goalw "fieldCI" ZF.thy [field_def] "(~ :r ==> : r) ==> a : field(r)" - (fn [prem]=> [ (fast_tac (!claset addIs [prem]) 1) ]); + (fn [prem]=> [ (blast_tac (!claset addIs [prem]) 1) ]); -qed_goalw "fieldE" thy [field_def] +qed_goalw "fieldE" ZF.thy [field_def] "[| a : field(r); \ \ !!x. : r ==> P; \ \ !!x. : r ==> P |] ==> P" @@ -114,40 +114,40 @@ AddIs [fieldCI]; AddSEs [fieldE]; -qed_goal "field_subset" thy "field(A*B) <= A Un B" - (fn _ => [ (Fast_tac 1) ]); +qed_goal "field_subset" ZF.thy "field(A*B) <= A Un B" + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "domain_subset_field" thy [field_def] +qed_goalw "domain_subset_field" ZF.thy [field_def] "domain(r) <= field(r)" (fn _ => [ (rtac Un_upper1 1) ]); -qed_goalw "range_subset_field" thy [field_def] +qed_goalw "range_subset_field" ZF.thy [field_def] "range(r) <= field(r)" (fn _ => [ (rtac Un_upper2 1) ]); -qed_goal "domain_times_range" thy +qed_goal "domain_times_range" ZF.thy "!!A B r. r <= Sigma(A,B) ==> r <= domain(r)*range(r)" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goal "field_times_field" thy +qed_goal "field_times_field" ZF.thy "!!A B r. r <= Sigma(A,B) ==> r <= field(r)*field(r)" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); (*** Image of a set under a function/relation ***) -qed_goalw "image_iff" thy [image_def] "b : r``A <-> (EX x:A. :r)" - (fn _ => [ (Fast_tac 1) ]); +qed_goalw "image_iff" ZF.thy [image_def] "b : r``A <-> (EX x:A. :r)" + (fn _ => [ (Blast_tac 1) ]); -qed_goal "image_singleton_iff" thy "b : r``{a} <-> :r" +qed_goal "image_singleton_iff" ZF.thy "b : r``{a} <-> :r" (fn _ => [ rtac (image_iff RS iff_trans) 1, - Fast_tac 1 ]); + Blast_tac 1 ]); -qed_goalw "imageI" thy [image_def] +qed_goalw "imageI" ZF.thy [image_def] "!!a b r. [| : r; a:A |] ==> b : r``A" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "imageE" thy [image_def] +qed_goalw "imageE" ZF.thy [image_def] "[| b: r``A; !!x.[| : r; x:A |] ==> P |] ==> P" (fn major::prems=> [ (rtac (major RS CollectE) 1), @@ -156,32 +156,32 @@ AddIs [imageI]; AddSEs [imageE]; -qed_goal "image_subset" thy "!!A B r. r <= A*B ==> r``C <= B" - (fn _ => [ (Fast_tac 1) ]); +qed_goal "image_subset" ZF.thy "!!A B r. r <= A*B ==> r``C <= B" + (fn _ => [ (Blast_tac 1) ]); (*** Inverse image of a set under a function/relation ***) -qed_goalw "vimage_iff" thy [vimage_def,image_def,converse_def] +qed_goalw "vimage_iff" ZF.thy [vimage_def,image_def,converse_def] "a : r-``B <-> (EX y:B. :r)" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goal "vimage_singleton_iff" thy +qed_goal "vimage_singleton_iff" ZF.thy "a : r-``{b} <-> :r" (fn _ => [ rtac (vimage_iff RS iff_trans) 1, - Fast_tac 1 ]); + Blast_tac 1 ]); -qed_goalw "vimageI" thy [vimage_def] +qed_goalw "vimageI" ZF.thy [vimage_def] "!!A B r. [| : r; b:B |] ==> a : r-``B" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -qed_goalw "vimageE" thy [vimage_def] +qed_goalw "vimageE" ZF.thy [vimage_def] "[| a: r-``B; !!x.[| : r; x:B |] ==> P |] ==> P" (fn major::prems=> [ (rtac (major RS imageE) 1), (REPEAT (etac converseD 1 ORELSE ares_tac prems 1)) ]); -qed_goalw "vimage_subset" thy [vimage_def] +qed_goalw "vimage_subset" ZF.thy [vimage_def] "!!A B r. r <= A*B ==> r-``C <= A" (fn _ => [ (etac (converse_type RS image_subset) 1) ]); @@ -194,22 +194,22 @@ val ZF_cs = !claset delrules [equalityI]; (** The Union of a set of relations is a relation -- Lemma for fun_Union **) -goal thy "!!S. (ALL x:S. EX A B. x <= A*B) ==> \ +goal ZF.thy "!!S. (ALL x:S. EX A B. x <= A*B) ==> \ \ Union(S) <= domain(Union(S)) * range(Union(S))"; -by (Fast_tac 1); +by (Blast_tac 1); qed "rel_Union"; (** The Union of 2 relations is a relation (Lemma for fun_Un) **) -qed_goal "rel_Un" thy +qed_goal "rel_Un" ZF.thy "!!r s. [| r <= A*B; s <= C*D |] ==> (r Un s) <= (A Un C) * (B Un D)" - (fn _ => [ (Fast_tac 1) ]); + (fn _ => [ (Blast_tac 1) ]); -goal thy "!!r. [| : r; c~=b |] ==> domain(r-{}) = domain(r)"; -by (Deepen_tac 0 1); +goal ZF.thy "!!r. [| : r; c~=b |] ==> domain(r-{}) = domain(r)"; +by (Blast_tac 1); qed "domain_Diff_eq"; -goal thy "!!r. [| : r; c~=a |] ==> range(r-{}) = range(r)"; -by (Deepen_tac 0 1); +goal ZF.thy "!!r. [| : r; c~=a |] ==> range(r-{}) = range(r)"; +by (Blast_tac 1); qed "range_Diff_eq";