let I, J be Program of SCM+FSA; :: thesis: dom I misses dom (ProgramPart (Relocated (J,(card I))))
assume A1: dom I meets dom (ProgramPart (Relocated (J,(card I)))) ; :: thesis: contradiction
dom (ProgramPart (Relocated (J,(card I)))) = dom (Reloc ((ProgramPart J),(card I))) by COMPOS_1:116
.= dom (Reloc (J,(card I))) by RELAT_1:209
.= dom (Shift (J,(card I))) by COMPOS_1:def 40
.= { (l + (card I)) where l is Element of NAT : l in dom J } by VALUED_1:def 12 ;
then consider x being set such that
A2: x in dom I and
A3: x in { (l + (card I)) where l is Element of NAT : l in dom J } by A1, XBOOLE_0:3;
consider l being Element of NAT such that
A4: x = l + (card I) and
l in dom J by A3;
l + (card I) < card I by A2, A4, AFINSQ_1:70;
hence contradiction by NAT_1:11; :: thesis: verum