theorem Th15:
  <*y\x*> ==>. (z\y)\(z\x)
proof
A1: <*y*>^<*y\x*> ==>. x by Th12;
  <*z*> ==>. z by Def18;
  then <*z*>^<*z\y*>^<*y\x*> ==>. x by A1,Lm6;
  then <*z*>^(<*z\y*>^<*y\x*>) ==>. x by FINSEQ_1:32;
  then <*z\y*>^<*y\x*> ==>. z\x by Def18;
  hence thesis by Def18;
end;
