reserve x,y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve R for Ring;
reserve G,H for LeftMod of R;
reserve V for LeftMod_DOMAIN of R;

theorem Th6:
  TrivialLMod(R) in LModObjects(UN,R)
proof
  set G0 = Trivial-addLoopStr, f0 = pr2(the carrier of R,{0});
   reconsider G0 as Element of GroupObjects(UN) by GRCAT_1:29;
   reconsider f0 as Element of Funcs([:the carrier of R,the carrier of G0:],
     the carrier of G0) by FUNCT_2:8;
  set x = [G0,f0];
A1:  x in the set of all
[G,f] where G is Element of GroupObjects(UN), f is Element
     of Funcs([:the carrier of R,the carrier of G:],
     the carrier of G) ;
   GO x,TrivialLMod(R),R;
  hence thesis by A1,Def6;
end;
