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 Th7:
  for x being Element of LModObjects(UN,R) holds x is strict LeftMod of R
proof
  let x be Element of LModObjects(UN,R);
  set N = 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) ;
  consider u being set such that
  u in N and
A1: GO u,x,R by Def6;
  ex a1,a2 being object st u = [a1,a2] & ex G being strict LeftMod of R st x
  = G & a1 = the addLoopStr of G & a2 = the lmult of G by A1;
  hence thesis;
end;
