
theorem Th16:
  for L being add-associative right_zeroed right_complementable
distributive non empty doubleLoopStr, x, y being Element of Polynom-Ring L, p
  , q be sequence of L st x = p & y = q holds x-y = p-q
proof
  let L being add-associative right_zeroed right_complementable distributive
non empty doubleLoopStr, x,y being Element of Polynom-Ring L, p,q be sequence
  of L;
  assume that
A1: x = p and
A2: y = q;
A3: -y = -q by A2,Th15;
  thus x - y = x + (-y) by RLVECT_1:def 11
    .= p - q by A1,A3,POLYNOM3:def 10;
end;
