set P = ((IC S),0) --> (0,(halt S));
A:
((IC S),0) --> (0,(halt S)) = (Start-At (0,S)) +* (0 .--> (halt S))
by FUNCT_4:def 4;
then reconsider P = ((IC S),0) --> (0,(halt S)) as FinPartState of S ;
take
P
; ( P is autonomic & not P is NAT -defined )
thus
P is autonomic
by Th12, A; not P is NAT -defined
dom P = {(IC S),0}
by FUNCT_4:65;
then A1:
IC S in dom P
by TARSKI:def 2;
not dom P c= NAT
by A1, COMPOS_1:3;
hence
not P is NAT -defined
by RELAT_1:def 18; verum