theorem
  <*>the carrier of s ==>. ((x/"z)/"(y/"z))/"(x/"y) &
  <*>the carrier of s ==>. (y\x)\((z\y)\(z\x))
proof
A1: <*x/"y*> ==>. (x/"z)/"(y/"z) by Th14;
  <*y\x*> ==>. (z\y)\(z\x) by Th15;
  hence thesis by A1,Th19;
end;
