reserve S,T,W,Y for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve Z for Subset of S;
reserve i,n for Nat;

theorem LM001:
  for S, T be RealNormSpace,
      L be LinearOperator of S, T,
      x, y be Point of S holds
    L.x - L.y = L.(x-y)
proof
  let S, T be RealNormSpace,
      L be LinearOperator of S, T,
      x, x0 be Point of S;
  thus L.x - L.x0 = L.x+(-1)*(L.x0) by RLVECT_1:16
  .= L.x+L.((-1)*x0) by LOPBAN_1:def 5
  .= L.(x+((-1)*x0)) by VECTSP_1:def 20
  .= L.(x-x0) by RLVECT_1:16;
end;
