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,M1,M,N
   for u be Homomorphism of R,M1,M holds
   tau(N,u) is Homomorphism of R, Hom(R,M,N), Hom(R,M1,N) by Def10;
