theorem
  <*x*(y/"z)*> ==>. (x*y)/"z :: and analogously <*z\y*x*> > z\(y*x)
proof
A1: <*x*> ==>. x by Def18;
  <*y*> ==>. y by Def18; then
A2: <*x*>^<*y*> ==>. x*y by A1,Def18;
  <*z*> ==>. z by Def18;
  then <*x*>^<*y/"z*>^<*z*> ==>. x*y by A2,Lm2;
  then <*x*(y/"z)*>^<*z*> ==>. x*y by Lm8;
  hence thesis by Def18;
end;
