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
    for R be comRing, M be LeftMod of R,a be Element of R holds
    (canHom(M)).a is Homomorphism of AbGr(M),AbGr(M)
    proof
      let R be comRing, M be LeftMod of R,a be Element of R;
      (canHom(M)).a in set_End(AbGr(M)); then
      consider f be Function of the carrier of AbGr(M), the carrier of AbGr(M)
      such that
A1:   f = (canHom(M)).a & f is Endomorphism of AbGr(M);
      thus thesis by A1;
    end;
