equal
deleted
inserted
replaced
8 Standard notation for Vset(i) is V(i), but users might want V for a variable |
8 Standard notation for Vset(i) is V(i), but users might want V for a variable |
9 *) |
9 *) |
10 |
10 |
11 Univ = Arith + Sum + "mono" + |
11 Univ = Arith + Sum + "mono" + |
12 consts |
12 consts |
13 Limit :: "i=>o" |
13 Vfrom :: "[i,i]=>i" |
14 Vfrom :: "[i,i]=>i" |
14 Vset :: "i=>i" |
15 Vset :: "i=>i" |
15 Vrec :: "[i, [i,i]=>i] =>i" |
16 Vrec :: "[i, [i,i]=>i] =>i" |
16 univ :: "i=>i" |
17 univ :: "i=>i" |
|
18 |
17 |
19 translations |
18 translations |
20 "Vset(x)" == "Vfrom(0,x)" |
19 "Vset(x)" == "Vfrom(0,x)" |
21 |
20 |
22 rules |
21 rules |
23 Limit_def "Limit(i) == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)" |
|
24 |
|
25 Vfrom_def "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))" |
22 Vfrom_def "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))" |
26 |
23 |
27 Vrec_def |
24 Vrec_def |
28 "Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)). \ |
25 "Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)). \ |
29 \ H(z, lam w:Vset(x). g`rank(w)`w)) ` a" |
26 \ H(z, lam w:Vset(x). g`rank(w)`w)) ` a" |