theorem
  <*x*> ==>. (x*y)/"y & <*x*> ==>. y\(y*x)
proof
A1: <*x*> ==>.x by Def18;
A2: <*y*> ==>.y by Def18;
  then
A3: <*x*>^<*y*> ==>. x*y by A1,Def18;
  <*y*>^<*x*> ==>. y*x by A1,A2,Def18;
  hence thesis by A3,Def18;
end;
