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
  x/"(z*y) <==>. (x/"y)/"z
proof
A1: <*z*> ==>. z by Def18;
A2: <*y*> ==>. y by Def18;
A3: <*x*> ==>. x by Def18;
  <*z*>^<*y*> ==>. z*y by A1,A2,Def18;
  then <*x/"(z*y)*>^(<*z*>^<*y*>) ==>. x by A3,Lm4;
  then <*x/"(z*y)*>^<*z*>^<*y*> ==>. x by FINSEQ_1:32;
  then <*x/"(z*y)*>^<*z*> ==>. x/"y by Def18;
  then
A4: <*x/"(z*y)*> ==>. (x/"y)/"z by Def18;
  <*x/"y*>^<*y*> ==>. x by A2,A3,Lm4;
  then <*(x/"y)/"z*>^<*z*>^<*y*> ==>. x by A1,Lm3;
  then <*(x/"y)/"z*>^<*z*y*> ==>. x by Lm9;
  then <*(x/"y)/"z*> ==>. x/"(z*y) by Def18;
  hence thesis by A4;
end;
