reserve x,y,z for Element of REAL+;

theorem Th27:
  not z <=' y & x <> {} implies [{},x *' (z -' y)] = (x *' y) - (x *' z)
proof
  assume ( not z <=' y)& x <> {};
  then
A1: not x *' z <=' x *' y by Lm2;
  thus [{},x *' (z -' y)] = [{},(x *' z) -' (x *' y)] by Lm14
    .= (x *' y) - (x *' z) by A1,Def2;
end;
