theorem Th15:
  -x < -y implies -(z => x) < -(z => y)
  proof
    assume
A1: -x < -y;
A2: -(z => x) < z "/\" (-x) by Def10;
    z "/\" (-x) < z "/\" (-y) by A1,Lm1; then
A3: -(z => x) < z "/\" (-y) by A2,Def3;
    z "/\" (-y) < -(z => y) by Def9;
    hence thesis by A3,Def3;
  end;
