reserve M,N for AbGroup;
 reserve R for Ring;
 reserve r for Element of R;
reserve M,N for LeftMod of R;
reserve f,g,h for Element of Funcs(the carrier of M, the carrier of N);
reserve a,b for Element of the carrier of R;
reserve R for comRing;
reserve M,M1,N,N1 for LeftMod of R;

theorem Th34:
    for f,g,h be Endomorphism of R,M st
    h = f*g
    holds AbGr(h) = (FuncComp(AbGr(M))).(AbGr(f),AbGr(g))
    proof
      let f,g,h be Endomorphism of R,M;
      assume h = f*g; then
      for x being Element of the carrier of AbGr(M) holds
      (AbGr(h)).x = ((AbGr(f))*(AbGr(g))).x by Lm33;
      hence thesis by Th29;
    end;
