FORMALIZED RECURSIVE FUNCTIONALS
15
Gp4(y): y=(y)0,(y)1,(y)2 & cpCCy^) & cP((y)2)&
(y)0=«^(y)o,o,i'(y)o,o,2 'A'B'^)0,3 &
(y)1)0=(y)0j0j2,(y)01,(y)02,(y)1,0,3 &
cp5a(y): y=(y)0,(y)1 & c p ^ ) & (y)0100 & (V)0fl1-o &
(y)0=«5,(y)0)0,i»(y)0,o,2 'A'B'(y)o,3 &
^)l,0^)0,0,l»2(7)0,1'°il-[Tli(y)0A)0Pi7)0,1'i,^^0)2^)0,3 -
cp5b(y): y=(y)0,(y)1,(y)2 & cP((y)1)& cp((y)2) & (y)0)1)0 o & ^)0,i,i ° &
(y)0=«5,(y)0,0,i'(y)o,o,2 J A'B ^^o,3 &
(y)lj0=(y)0)0, t(y)oA/3:,(y)02,(y)lf0#3 &
n3i-(7)o,l,o,Pi
' ^0,2'^0,3^
cp6(y): y=(y)0,(y)1 & GpCCy)^ &
(y)0,i,o(y)o,o,2&
(y)0=«^(y)0,0,i»^ o ^ '
5
'
(y)o,3 &
, \ _w i (y)o,l,0
/T
-r (y)o.l.i'
S ^ W '
2
*(iL(y)
n
002
P i )•
(y)o,i,i
, n (y)o,i,i / N / N ^
Cp?(y): y=(y)0 & (jr)0^?o
&
^o^O
5 0 &
(^Wo i i ^
&
(y)0=«7,A,B,((y)0^A)(y)o
i
^1.
CP8(y)s y-Zj^Wf & CP((yy & (7)0,2,0^)0,0,2
&
(y)0««8,(y)0,o,i*(y)o,o,2 'A'B*(y)o,3 &
(y)l,0=(y)0,0,l(y)o,l^(y)0'2'0-(n"li(y)0j0)2pf)0'2'i
^y)0,2,1'*n(y)
»a(y) Pi^
0
'
2
'
1
.^^-
Nowj as we said we would, we undertake to pick a standard formula Cp(y),
containing free only y, such that Gp(y) ~ CpQ (y) V ..• V Cpg(y) (i.e. (1)
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