reserve s for non empty typealg,
  T,X,Y,T9,X9,Y9 for FinSequence of s,
  x,y,z,y9,z9 for type of s;
reserve Tr for PreProof of s;
reserve p for Proof of s,
  v for Element of dom p;
reserve A for non empty set,
  a,a1,a2,b for Element of A*;
reserve s for non empty typestr,
  x for type of s;
reserve s for SynTypes_Calculus,
  T,X,Y for FinSequence of s,
  x,y,z for type of s;

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;
