theorem
 for k being Nat st k < LastLoc I
  holds (I ';' J).k = I.k
proof let k be Nat;
 assume k < LastLoc I;
  then
A1: k in dom CutLastLoc I by Th26;
  dom CutLastLoc I misses dom Reloc(J,card I -' 1) by COMPOS_1:18;
  then not k in dom Reloc(J,card I -' 1) by A1,XBOOLE_0:3;
 hence (I ';' J).k = (CutLastLoc I).k by FUNCT_4:11
      .= I.k by A1,GRFUNC_1:2;
end;
