theorem
  dom I misses dom Reloc(J, card I)
proof
  assume
A1: dom I meets dom Reloc(J, card I);
  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;
end;
