let S be COM-Struct ; :: thesis: for I, J being Program of S holds dom I misses dom (Reloc (J,(card I)))
let I, J be Program of S; :: thesis: dom I misses dom (Reloc (J,(card I)))
assume A1: dom I meets dom (Reloc (J,(card I))) ; :: thesis: contradiction
dom (Reloc (J,(card I))) = dom (Shift (J,(card I))) by Th20
.= { (l + (card I)) where l is Nat : l in dom J } by VALUED_1:def 12 ;
then consider x being object such that
A2: x in dom I and
A3: x in { (l + (card I)) where l is Nat : l in dom J } by A1, XBOOLE_0:3;
consider l being Nat such that
A4: x = l + (card I) and
l in dom J by A3;
l + (card I) < card I by A2, A4, AFINSQ_1:66;
hence contradiction by NAT_1:11; :: thesis: verum