# HG changeset patch # User traytel # Date 1373040607 -7200 # Node ID 0c4b140cff00533c475908e2ad52435ca4065e2f # Parent 6f5678b97c4ecef3d78fd9987bda4b953a611983 tuned spelling diff -r 6f5678b97c4e -r 0c4b140cff00 src/HOL/BNF/More_BNFs.thy --- a/src/HOL/BNF/More_BNFs.thy Sat Jul 06 22:16:55 2013 +0200 +++ b/src/HOL/BNF/More_BNFs.thy Fri Jul 05 18:10:07 2013 +0200 @@ -391,7 +391,7 @@ next case False hence "|{X. X \ A \ countable X}| =o |{X. X \ A \ countable X} - {{}}|" - by (intro card_of_infinite_diff_finitte finite.emptyI finite.insertI ordIso_symmetric) + by (intro card_of_infinite_diff_finite finite.emptyI finite.insertI ordIso_symmetric) (unfold finite_countable_subset) also have "|{X. X \ A \ countable X} - {{}}| \o |A| ^c natLeq" using card_of_countable_sets_Func[of A] unfolding set_diff_eq by auto diff -r 6f5678b97c4e -r 0c4b140cff00 src/HOL/Cardinals/Cardinal_Order_Relation.thy --- a/src/HOL/Cardinals/Cardinal_Order_Relation.thy Sat Jul 06 22:16:55 2013 +0200 +++ b/src/HOL/Cardinals/Cardinal_Order_Relation.thy Fri Jul 05 18:10:07 2013 +0200 @@ -997,7 +997,7 @@ lemma infinite_card_of_diff_singl: assumes "infinite A" shows "|A - {a}| =o |A|" -by (metis assms card_of_infinite_diff_finitte finite.emptyI finite_insert) +by (metis assms card_of_infinite_diff_finite finite.emptyI finite_insert) lemma card_of_vimage: assumes "B \ range f" @@ -1066,7 +1066,7 @@ moreover {have 2: "infinite (Bpow r A)" using infinite_Bpow[OF rc r A] . have "|Bpow r A| =o |Bpow r A - {{}}|" - using card_of_infinite_diff_finitte + using card_of_infinite_diff_finite by (metis Pow_empty 2 finite_Pow_iff infinite_imp_nonempty ordIso_symmetric) } ultimately show ?thesis by (metis ordIso_ordLeq_trans) diff -r 6f5678b97c4e -r 0c4b140cff00 src/HOL/Cardinals/Cardinal_Order_Relation_Base.thy --- a/src/HOL/Cardinals/Cardinal_Order_Relation_Base.thy Sat Jul 06 22:16:55 2013 +0200 +++ b/src/HOL/Cardinals/Cardinal_Order_Relation_Base.thy Fri Jul 05 18:10:07 2013 +0200 @@ -2199,8 +2199,7 @@ subsection {* Others *} -(* FIXME: finitte ~> finite? *) -lemma card_of_infinite_diff_finitte: +lemma card_of_infinite_diff_finite: assumes "infinite A" and "finite B" shows "|A - B| =o |A|" by (metis assms card_of_Un_diff_infinite finite_ordLess_infinite2) @@ -2294,8 +2293,7 @@ qed qed -(* FIXME: betwe ~> betw? *) -lemma bij_betwe_curr: +lemma bij_betw_curr: "bij_betw (curr A) (Func (A <*> B) C) (Func A (Func B C))" unfolding bij_betw_def inj_on_def image_def using curr_in curr_inj curr_surj by blast @@ -2303,7 +2301,7 @@ lemma card_of_Func_Times: "|Func (A <*> B) C| =o |Func A (Func B C)|" unfolding card_of_ordIso[symmetric] -using bij_betwe_curr by blast +using bij_betw_curr by blast definition Func_map where "Func_map B2 f1 f2 g b2 \