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 (IncAddr (Shift (ProgramPart J),(card I)),(card I)) by SCMFSA_5:2
.= dom (IncAddr (Shift J,(card I)),(card I)) by AMI_1:105
.= dom (Shift J,(card I)) by SCMFSA_4:def 6
.= { (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, Th15;
hence contradiction by NAT_1:11; :: thesis: verum