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
  <*>the carrier of s ==>. (y/"(x\y))/"x &
  <*>the carrier of s ==>. x\((y/"x)\ y )
proof
A1: <*x*> ==>. y/"(x\y) by Th13;
  <*x*> ==>. (y/"x)\y by Th13;
  hence thesis by A1,Th19;
end;
