reserve R for Ring, S for R-monomorphic Ring,
        K for Field, F for K-monomorphic Field,
        T for K-monomorphic comRing;

theorem Th4:
   for f being Monomorphism of R,S, a being Element of R
   holds f.a = 0.S iff a = 0.R
   proof
     let f be Monomorphism of R,S, a be Element of R;
     now assume f.a = 0.S; then
       f.a = f.(0.R) by RING_2:6;
       hence a = 0.R by FUNCT_2:19;
     end;
     hence thesis by RING_2:6;
   end;
