reserve L for non empty doubleLoopStr;
reserve a,b,c,x,y,z for Element of L;
reserve G for left-distributive doubleLoop,
  a,b,x,y for Element of G;

theorem
  (x-y)*a = x*a - y*a
proof
  thus (x-y)*a = x*a + (-y)*a by VECTSP_1:def 3
    .= x*a - y*a by Th7;
end;
