src/ZF/AC/AC18_AC19.thy
changeset 12820 02e2ff3e4d37
parent 12776 249600a63ba9
child 13339 0f89104dd377
equal deleted inserted replaced
12819:2f61bca07de7 12820:02e2ff3e4d37
    64 apply (blast dest!: sym [THEN RepFun_eq_0_iff [THEN iffD1]])
    64 apply (blast dest!: sym [THEN RepFun_eq_0_iff [THEN iffD1]])
    65 done
    65 done
    66 
    66 
    67 lemma lemma1_1: "[|c \<in> a; x = c Un {0}; x \<notin> a |] ==> x - {0} \<in> a"
    67 lemma lemma1_1: "[|c \<in> a; x = c Un {0}; x \<notin> a |] ==> x - {0} \<in> a"
    68 apply clarify 
    68 apply clarify 
    69 apply (rule subst_elem , (assumption))
    69 apply (rule subst_elem, assumption)
    70 apply (fast elim: notE subst_elem)
    70 apply (fast elim: notE subst_elem)
    71 done
    71 done
    72 
    72 
    73 lemma lemma1_2: 
    73 lemma lemma1_2: 
    74         "[| f`(uu(a)) \<notin> a; f \<in> (\<Pi>B \<in> {uu(a). a \<in> A}. B); a \<in> A |]   
    74         "[| f`(uu(a)) \<notin> a; f \<in> (\<Pi>B \<in> {uu(a). a \<in> A}. B); a \<in> A |]   
    96 lemma AC19_AC1: "AC19 ==> AC1"
    96 lemma AC19_AC1: "AC19 ==> AC1"
    97 apply (unfold AC19_def AC1_def, clarify)
    97 apply (unfold AC19_def AC1_def, clarify)
    98 apply (case_tac "A=0", force)
    98 apply (case_tac "A=0", force)
    99 apply (erule_tac x = "{uu (a) . a \<in> A}" in allE)
    99 apply (erule_tac x = "{uu (a) . a \<in> A}" in allE)
   100 apply (erule impE)
   100 apply (erule impE)
   101 apply (erule RepRep_conj , (assumption))
   101 apply (erule RepRep_conj, assumption)
   102 apply (rule lemma1)
   102 apply (rule lemma1)
   103 apply (drule lemma2 , (assumption))
   103 apply (drule lemma2, assumption, auto) 
   104 apply auto 
       
   105 done
   104 done
   106 
   105 
   107 end
   106 end