avoid duplicate fact bindings;
authorwenzelm
Tue Aug 27 11:09:33 2002 +0200 (2002-08-27)
changeset 13534ca6debb89d77
parent 13533 70de987e9fe3
child 13535 007559e981c7
avoid duplicate fact bindings;
src/ZF/Ordinal.thy
src/ZF/QPair.thy
src/ZF/Trancl.thy
src/ZF/Univ.thy
src/ZF/WF.thy
     1.1 --- a/src/ZF/Ordinal.thy	Tue Aug 27 11:07:54 2002 +0200
     1.2 +++ b/src/ZF/Ordinal.thy	Tue Aug 27 11:09:33 2002 +0200
     1.3 @@ -328,11 +328,12 @@
     1.4  done
     1.5  
     1.6  (*Induction over an ordinal*)
     1.7 -lemmas Ord_induct = Transset_induct [OF _ Ord_is_Transset]
     1.8 +lemmas Ord_induct [consumes 2] = Transset_induct [OF _ Ord_is_Transset]
     1.9 +lemmas Ord_induct_rule = Ord_induct [rule_format, consumes 2]
    1.10  
    1.11  (*Induction over the class of ordinals -- a useful corollary of Ord_induct*)
    1.12  
    1.13 -lemma trans_induct:
    1.14 +lemma trans_induct [consumes 1]:
    1.15      "[| Ord(i);  
    1.16          !!x.[| Ord(x);  ALL y:x. P(y) |] ==> P(x) |]
    1.17       ==>  P(i)"
    1.18 @@ -340,6 +341,8 @@
    1.19  apply (blast intro: Ord_succ [THEN Ord_in_Ord]) 
    1.20  done
    1.21  
    1.22 +lemmas trans_induct_rule = trans_induct [rule_format, consumes 1]
    1.23 +
    1.24  
    1.25  (*** Fundamental properties of the epsilon ordering (< on ordinals) ***)
    1.26  
    1.27 @@ -684,7 +687,7 @@
    1.28       |] ==> P"
    1.29  by (drule Ord_cases_disj, blast)  
    1.30  
    1.31 -lemma trans_induct3:
    1.32 +lemma trans_induct3 [case_names 0 succ limit, consumes 1]:
    1.33       "[| Ord(i);                 
    1.34           P(0);                   
    1.35           !!x. [| Ord(x);  P(x) |] ==> P(succ(x));        
    1.36 @@ -694,6 +697,8 @@
    1.37  apply (erule Ord_cases, blast+)
    1.38  done
    1.39  
    1.40 +lemmas trans_induct3_rule = trans_induct3 [rule_format, case_names 0 succ limit, consumes 1]
    1.41 +
    1.42  text{*A set of ordinals is either empty, contains its own union, or its
    1.43  union is a limit ordinal.*}
    1.44  lemma Ord_set_cases:
    1.45 @@ -721,14 +726,6 @@
    1.46  apply (blast intro!: equalityI)
    1.47  done
    1.48  
    1.49 -(*special induction rules for the "induct" method*)
    1.50 -lemmas Ord_induct = Ord_induct [consumes 2]
    1.51 -  and Ord_induct_rule = Ord_induct [rule_format, consumes 2]
    1.52 -  and trans_induct = trans_induct [consumes 1]
    1.53 -  and trans_induct_rule = trans_induct [rule_format, consumes 1]
    1.54 -  and trans_induct3 = trans_induct3 [case_names 0 succ limit, consumes 1]
    1.55 -  and trans_induct3_rule = trans_induct3 [rule_format, case_names 0 succ limit, consumes 1]
    1.56 -
    1.57  ML 
    1.58  {*
    1.59  val Memrel_def = thm "Memrel_def";
     2.1 --- a/src/ZF/QPair.thy	Tue Aug 27 11:07:54 2002 +0200
     2.2 +++ b/src/ZF/QPair.thy	Tue Aug 27 11:09:33 2002 +0200
     2.3 @@ -93,13 +93,6 @@
     2.4  by (simp add: QSigma_def)
     2.5  
     2.6  
     2.7 -(*The general elimination rule*)
     2.8 -lemma QSigmaE:
     2.9 -    "[| c: QSigma(A,B);   
    2.10 -        !!x y.[| x:A;  y:B(x);  c=<x;y> |] ==> P  
    2.11 -     |] ==> P"
    2.12 -by (simp add: QSigma_def, blast) 
    2.13 -
    2.14  (** Elimination rules for <a;b>:A*B -- introducing no eigenvariables **)
    2.15  
    2.16  lemma QSigmaE [elim!]:
     3.1 --- a/src/ZF/Trancl.thy	Tue Aug 27 11:07:54 2002 +0200
     3.2 +++ b/src/ZF/Trancl.thy	Tue Aug 27 11:09:33 2002 +0200
     3.3 @@ -49,7 +49,7 @@
     3.4      "[| !!x. x:A ==> <x,x> ~: r |] ==> irrefl(A,r)"
     3.5  by (simp add: irrefl_def) 
     3.6  
     3.7 -lemma symI: "[| irrefl(A,r);  x:A |] ==>  <x,x> ~: r"
     3.8 +lemma irreflE: "[| irrefl(A,r);  x:A |] ==>  <x,x> ~: r"
     3.9  by (simp add: irrefl_def)
    3.10  
    3.11  subsubsection{*symmetry*}
    3.12 @@ -58,7 +58,7 @@
    3.13       "[| !!x y.<x,y>: r ==> <y,x>: r |] ==> sym(r)"
    3.14  by (unfold sym_def, blast) 
    3.15  
    3.16 -lemma antisymI: "[| sym(r); <x,y>: r |]  ==>  <y,x>: r"
    3.17 +lemma symE: "[| sym(r); <x,y>: r |]  ==>  <y,x>: r"
    3.18  by (unfold sym_def, blast)
    3.19  
    3.20  subsubsection{*antisymmetry*}
    3.21 @@ -139,7 +139,7 @@
    3.22  
    3.23  (** standard induction rule **)
    3.24  
    3.25 -lemma rtrancl_full_induct:
    3.26 +lemma rtrancl_full_induct [case_names initial step, consumes 1]:
    3.27    "[| <a,b> : r^*;  
    3.28        !!x. x: field(r) ==> P(<x,x>);  
    3.29        !!x y z.[| P(<x,y>); <x,y>: r^*; <y,z>: r |]  ==>  P(<x,z>) |]  
    3.30 @@ -149,7 +149,7 @@
    3.31  (*nice induction rule.
    3.32    Tried adding the typing hypotheses y,z:field(r), but these
    3.33    caused expensive case splits!*)
    3.34 -lemma rtrancl_induct:
    3.35 +lemma rtrancl_induct [case_names initial step, induct set: rtrancl]:
    3.36    "[| <a,b> : r^*;                                               
    3.37        P(a);                                                      
    3.38        !!y z.[| <a,y> : r^*;  <y,z> : r;  P(y) |] ==> P(z)        
    3.39 @@ -228,7 +228,7 @@
    3.40  done
    3.41  
    3.42  (*Nice induction rule for trancl*)
    3.43 -lemma trancl_induct:
    3.44 +lemma trancl_induct [case_names initial step, induct set: trancl]:
    3.45    "[| <a,b> : r^+;                                       
    3.46        !!y.  [| <a,y> : r |] ==> P(y);                    
    3.47        !!y z.[| <a,y> : r^+;  <y,z> : r;  P(y) |] ==> P(z)        
    3.48 @@ -353,7 +353,7 @@
    3.49  apply (safe dest!: trancl_converseD intro!: trancl_converseI)
    3.50  done
    3.51  
    3.52 -lemma converse_trancl_induct:
    3.53 +lemma converse_trancl_induct [case_names initial step, consumes 1]:
    3.54  "[| <a, b>:r^+; !!y. <y, b> :r ==> P(y);  
    3.55        !!y z. [| <y, z> : r; <z, b> : r^+; P(z) |] ==> P(y) |]  
    3.56         ==> P(a)"
    3.57 @@ -363,12 +363,6 @@
    3.58  apply (auto simp add: trancl_converse)
    3.59  done
    3.60  
    3.61 -lemmas rtrancl_induct = rtrancl_induct [case_names initial step, induct set: rtrancl]
    3.62 -  and trancl_induct = trancl_induct [case_names initial step, induct set: trancl]
    3.63 -  and converse_trancl_induct = converse_trancl_induct [case_names initial step, consumes 1]
    3.64 -  and rtrancl_full_induct = rtrancl_full_induct [case_names initial step, consumes 1]
    3.65 -
    3.66 -
    3.67  ML
    3.68  {*
    3.69  val refl_def = thm "refl_def";
     4.1 --- a/src/ZF/Univ.thy	Tue Aug 27 11:07:54 2002 +0200
     4.2 +++ b/src/ZF/Univ.thy	Tue Aug 27 11:09:33 2002 +0200
     4.3 @@ -192,8 +192,6 @@
     4.4  apply (blast intro: ltI Limit_is_Ord)
     4.5  done
     4.6  
     4.7 -lemmas zero_in_VLimit = Limit_has_0 [THEN ltD, THEN zero_in_Vfrom, standard]
     4.8 -
     4.9  lemma singleton_in_VLimit:
    4.10      "[| a \<in> Vfrom(A,i);  Limit(i) |] ==> {a} \<in> Vfrom(A,i)"
    4.11  apply (erule Limit_VfromE, assumption)
     5.1 --- a/src/ZF/WF.thy	Tue Aug 27 11:07:54 2002 +0200
     5.2 +++ b/src/ZF/WF.thy	Tue Aug 27 11:09:33 2002 +0200
     5.3 @@ -100,7 +100,7 @@
     5.4  (** Well-founded Induction **)
     5.5  
     5.6  (*Consider the least z in domain(r) such that P(z) does not hold...*)
     5.7 -lemma wf_induct:
     5.8 +lemma wf_induct [induct set: wf]:
     5.9      "[| wf(r);
    5.10          !!x.[| ALL y. <y,x>: r --> P(y) |] ==> P(x)
    5.11       |]  ==>  P(a)"
    5.12 @@ -109,9 +109,7 @@
    5.13  apply blast 
    5.14  done
    5.15  
    5.16 -(*fixed up for induct method*)
    5.17 -lemmas wf_induct = wf_induct [induct set: wf]
    5.18 -  and wf_induct_rule = wf_induct [rule_format, induct set: wf]
    5.19 +lemmas wf_induct_rule = wf_induct [rule_format, induct set: wf]
    5.20  
    5.21  (*The form of this rule is designed to match wfI*)
    5.22  lemma wf_induct2:
    5.23 @@ -125,7 +123,7 @@
    5.24  lemma field_Int_square: "field(r Int A*A) <= A"
    5.25  by blast
    5.26  
    5.27 -lemma wf_on_induct:
    5.28 +lemma wf_on_induct [consumes 2, induct set: wf_on]:
    5.29      "[| wf[A](r);  a:A;
    5.30          !!x.[| x: A;  ALL y:A. <y,x>: r --> P(y) |] ==> P(x)
    5.31       |]  ==>  P(a)"
    5.32 @@ -134,10 +132,8 @@
    5.33  apply (rule field_Int_square, blast)
    5.34  done
    5.35  
    5.36 -(*fixed up for induct method*)
    5.37 -lemmas wf_on_induct = wf_on_induct [consumes 2, induct set: wf_on]
    5.38 -   and wf_on_induct_rule = 
    5.39 -	 wf_on_induct [rule_format, consumes 2, induct set: wf_on]
    5.40 +lemmas wf_on_induct_rule =
    5.41 +  wf_on_induct [rule_format, consumes 2, induct set: wf_on]
    5.42  
    5.43  
    5.44  (*If r allows well-founded induction then wf(r)*)