diff -r faacfd4392b5 -r 5a5c8ea5f66a src/ZF/Constructible/DPow_absolute.thy --- a/src/ZF/Constructible/DPow_absolute.thy Tue Nov 07 19:39:54 2006 +0100 +++ b/src/ZF/Constructible/DPow_absolute.thy Tue Nov 07 19:40:13 2006 +0100 @@ -23,7 +23,7 @@ successor(M,dp,i) & fun_apply(M,f,p,z) & is_transrec(M,MH,i,f)" *) -constdefs formula_rec_fm :: "[i, i, i]=>i" +definition formula_rec_fm :: "[i, i, i]=>i" "formula_rec_fm(mh,p,z) == Exists(Exists(Exists( And(finite_ordinal_fm(2), @@ -80,7 +80,7 @@ subsubsection{*The Operator @{term is_satisfies}*} (* is_satisfies(M,A,p,z) == is_formula_rec (M, satisfies_MH(M,A), p, z) *) -constdefs satisfies_fm :: "[i,i,i]=>i" +definition satisfies_fm :: "[i,i,i]=>i" "satisfies_fm(x) == formula_rec_fm (satisfies_MH_fm(x#+5#+6, 2, 1, 0))" lemma is_satisfies_type [TC]: @@ -119,7 +119,7 @@ text{*Relativize the use of @{term sats} within @{term DPow'} (the comprehension).*} -constdefs +definition is_DPow_sats :: "[i=>o,i,i,i,i] => o" "is_DPow_sats(M,A,env,p,x) == \n1[M]. \e[M]. \sp[M]. @@ -148,7 +148,7 @@ is_satisfies(M,A,p,sp) --> is_Cons(M,x,env,e) --> fun_apply(M, sp, e, n1) --> number1(M, n1) *) -constdefs DPow_sats_fm :: "[i,i,i,i]=>i" +definition DPow_sats_fm :: "[i,i,i,i]=>i" "DPow_sats_fm(A,env,p,x) == Forall(Forall(Forall( Implies(satisfies_fm(A#+3,p#+3,0), @@ -218,7 +218,7 @@ done text{*Relativization of the Operator @{term DPow'}*} -constdefs +definition is_DPow' :: "[i=>o,i,i] => o" "is_DPow'(M,A,Z) == \X[M]. X \ Z <-> @@ -310,7 +310,7 @@ (* is_Collect :: "[i=>o,i,i=>o,i] => o" "is_Collect(M,A,P,z) == \x[M]. x \ z <-> x \ A & P(x)" *) -constdefs Collect_fm :: "[i, i, i]=>i" +definition Collect_fm :: "[i, i, i]=>i" "Collect_fm(A,is_P,z) == Forall(Iff(Member(0,succ(z)), And(Member(0,succ(A)), is_P)))" @@ -360,7 +360,7 @@ (* is_Replace :: "[i=>o,i,[i,i]=>o,i] => o" "is_Replace(M,A,P,z) == \u[M]. u \ z <-> (\x[M]. x\A & P(x,u))" *) -constdefs Replace_fm :: "[i, i, i]=>i" +definition Replace_fm :: "[i, i, i]=>i" "Replace_fm(A,is_P,z) == Forall(Iff(Member(0,succ(z)), Exists(And(Member(0,A#+2), is_P))))" @@ -413,7 +413,7 @@ (\env[M]. \p[M]. mem_formula(M,p) & mem_list(M,A,env) & is_Collect(M, A, is_DPow_sats(M,A,env,p), X))" *) -constdefs DPow'_fm :: "[i,i]=>i" +definition DPow'_fm :: "[i,i]=>i" "DPow'_fm(A,Z) == Forall( Iff(Member(0,succ(Z)), @@ -451,7 +451,7 @@ subsection{*A Locale for Relativizing the Operator @{term Lset}*} -constdefs +definition transrec_body :: "[i=>o,i,i,i,i] => o" "transrec_body(M,g,x) == \y z. \gy[M]. y \ x & fun_apply(M,g,y,gy) & is_DPow'(M,gy,z)" @@ -503,7 +503,7 @@ text{*Relativization of the Operator @{term Lset}*} -constdefs +definition is_Lset :: "[i=>o, i, i] => o" --{*We can use the term language below because @{term is_Lset} will not have to be internalized: it isn't used in any instance of @@ -609,7 +609,7 @@ subsection{*The Notion of Constructible Set*} -constdefs +definition constructible :: "[i=>o,i] => o" "constructible(M,x) == \i[M]. \Li[M]. ordinal(M,i) & is_Lset(M,i,Li) & x \ Li"