theorem Lm63:
   Non_ZeroDiv_Set(A) = [#]A \ {0.A} & Non_ZeroDiv_Set(A) is
   without_zero non empty multiplicatively-closed Subset of A
   proof
A1:  Non_ZeroDiv_Set(A) = [#]A \ {0.A} by Th4;
     0.A in [#]A & 0.A in {0.A} by TARSKI:def 1; then
     Non_ZeroDiv_Set(A) is without_zero by A1, XBOOLE_0:def 5;
     hence thesis by Th4;
   end;
