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 holds
   M ~= AbGrLMod(AbGr(M),canHom(M))
   proof
     let R be comRing, M be LeftMod of R;
A1:  rho(M) is Homomorphism of R,M,AbGrLMod(AbGr(M),canHom(M)) by Def10;
     rho(M) is one-to-one onto by Th38;
     hence thesis by A1;
   end;
