theorem Th7:
  [x,y] in FreeAtoms(M0) iff x in dom M0 & y in (Carrier M0).x
proof
  hereby
    assume [x,y] in FreeAtoms(M0);
    then x in dom Carrier M0 & y in (Carrier M0).x by WAYBEL26:38;
    hence x in dom M0 & y in (Carrier M0).x by PRALG_1:def 14;
  end;
  assume A1: x in dom M0 & y in (Carrier M0).x;
  then x in dom Carrier M0 by PRALG_1:def 14;
  hence thesis by A1, WAYBEL26:38;
end;
