reserve V for non empty RLSStruct;
reserve x,y,y1 for set;
reserve v for VECTOR of V;
reserve a,b for Real;

theorem Th4:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v being Element of V holds v + 0.V = v & 0.V + v = v
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr, v be Element of V;
  consider w being Element of V such that
A1: v + w = 0.V by ALGSTR_0:def 11;
  thus
A2: v + 0.V = v by Def4;
  w + v = 0.V by A1,Lm1;
  hence thesis by A2,A1,Def3;
end;
