src/ZF/Constructible/Wellorderings.thy
changeset 13293 09276ee04361
parent 13269 3ba9be497c33
child 13295 ca2e9b273472
     1.1 --- a/src/ZF/Constructible/Wellorderings.thy	Thu Jul 04 10:53:52 2002 +0200
     1.2 +++ b/src/ZF/Constructible/Wellorderings.thy	Thu Jul 04 10:54:04 2002 +0200
     1.3 @@ -346,23 +346,23 @@
     1.4    obase :: "[i=>o,i,i,i] => o"
     1.5         --{*the domain of @{text om}, eventually shown to equal @{text A}*}
     1.6     "obase(M,A,r,z) == 
     1.7 -	\<forall>a. M(a) --> 
     1.8 -         (a \<in> z <-> 
     1.9 +	\<forall>a[M]. 
    1.10 +         a \<in> z <-> 
    1.11            (a\<in>A & (\<exists>x g mx par. M(x) & M(g) & M(mx) & M(par) & ordinal(M,x) & 
    1.12                                 membership(M,x,mx) & pred_set(M,A,a,r,par) &  
    1.13 -                               order_isomorphism(M,par,r,x,mx,g))))"
    1.14 +                               order_isomorphism(M,par,r,x,mx,g)))"
    1.15  
    1.16  
    1.17    omap :: "[i=>o,i,i,i] => o"  
    1.18      --{*the function that maps wosets to order types*}
    1.19     "omap(M,A,r,f) == 
    1.20 -	\<forall>z. M(z) --> 
    1.21 -         (z \<in> f <-> 
    1.22 +	\<forall>z[M].
    1.23 +         z \<in> f <-> 
    1.24            (\<exists>a\<in>A. M(a) & 
    1.25             (\<exists>x g mx par. M(x) & M(g) & M(mx) & M(par) & ordinal(M,x) & 
    1.26                           pair(M,a,x,z) & membership(M,x,mx) & 
    1.27                           pred_set(M,A,a,r,par) &  
    1.28 -                         order_isomorphism(M,par,r,x,mx,g))))"
    1.29 +                         order_isomorphism(M,par,r,x,mx,g)))"
    1.30  
    1.31  
    1.32    otype :: "[i=>o,i,i,i] => o"  --{*the order types themselves*}
    1.33 @@ -392,8 +392,10 @@
    1.34                     g \<in> ord_iso(Order.pred(A,a,r),r,x,Memrel(x)))"
    1.35  apply (rotate_tac 1) 
    1.36  apply (simp add: omap_def Memrel_closed pred_closed) 
    1.37 -apply (rule iffI) 
    1.38 -apply (drule_tac x=z in spec, blast dest: transM)+ 
    1.39 +apply (rule iffI)
    1.40 + apply (drule_tac [2] x=z in rspec)
    1.41 + apply (drule_tac x=z in rspec)
    1.42 + apply (blast dest: transM)+
    1.43  done
    1.44  
    1.45  lemma (in M_axioms) omap_unique:
    1.46 @@ -576,35 +578,37 @@
    1.47         M(A); M(r); M(f); M(B); M(i) |] ==> f \<in> ord_iso(A, r, i, Memrel(i))"
    1.48  apply (frule omap_ord_iso, assumption+) 
    1.49  apply (frule obase_equals, assumption+, blast) 
    1.50 -done
    1.51 +done 
    1.52  
    1.53  lemma (in M_axioms) obase_exists:
    1.54 -     "[| M(A); M(r) |] ==> \<exists>z. M(z) & obase(M,A,r,z)"
    1.55 +     "[| M(A); M(r) |] ==> \<exists>z[M]. obase(M,A,r,z)"
    1.56  apply (simp add: obase_def) 
    1.57  apply (insert obase_separation [of A r])
    1.58  apply (simp add: separation_def)  
    1.59  done
    1.60  
    1.61  lemma (in M_axioms) omap_exists:
    1.62 -     "[| M(A); M(r) |] ==> \<exists>z. M(z) & omap(M,A,r,z)"
    1.63 +     "[| M(A); M(r) |] ==> \<exists>z[M]. omap(M,A,r,z)"
    1.64  apply (insert obase_exists [of A r]) 
    1.65  apply (simp add: omap_def) 
    1.66  apply (insert omap_replacement [of A r])
    1.67  apply (simp add: strong_replacement_def, clarify) 
    1.68 -apply (drule_tac x=z in spec, clarify) 
    1.69 +apply (drule_tac x=x in spec, clarify) 
    1.70  apply (simp add: Memrel_closed pred_closed obase_iff)
    1.71  apply (erule impE) 
    1.72   apply (clarsimp simp add: univalent_def)
    1.73   apply (blast intro: Ord_iso_implies_eq ord_iso_sym ord_iso_trans, clarify)  
    1.74 -apply (rule_tac x=Y in exI) 
    1.75 -apply (simp add: Memrel_closed pred_closed obase_iff, blast)   
    1.76 +apply (rule_tac x=Y in rexI) 
    1.77 +apply (simp add: Memrel_closed pred_closed obase_iff, blast, assumption)
    1.78  done
    1.79  
    1.80 +declare rall_simps [simp] rex_simps [simp]
    1.81 +
    1.82  lemma (in M_axioms) otype_exists:
    1.83       "[| wellordered(M,A,r); M(A); M(r) |] ==> \<exists>i. M(i) & otype(M,A,r,i)"
    1.84 -apply (insert omap_exists [of A r]) 
    1.85 -apply (simp add: otype_def, clarify) 
    1.86 -apply (rule_tac x="range(z)" in exI) 
    1.87 +apply (insert omap_exists [of A r])  
    1.88 +apply (simp add: otype_def, safe)
    1.89 +apply (rule_tac x="range(x)" in exI) 
    1.90  apply blast 
    1.91  done
    1.92