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

theorem Th3:
  for V being add-associative right_zeroed right_complementable
  addLoopStr holds V is right_add-cancelable
proof
  let V being add-associative right_zeroed right_complementable addLoopStr;
  let v being Element of V;
  consider v1 being Element of V such that
A1: v + v1 = 0.V by ALGSTR_0:def 11;
  let u, w be Element of V;
  assume
A2: u + v = w + v;
  thus u = u + 0.V by Def4
    .= u + v + v1 by A1,Def3
    .= w + 0.V by A1,A2,Def3
    .= w by Def4;
end;
