theorem
  x*y*z <==>. x*(y*z)
proof
A1: <*x*> ==>. x by Def18;
A2: <*y*> ==>. y by Def18;
A3: <*z*> ==>. z by Def18;
  <*x*>^<*y*> ==>. x*y by A1,A2,Def18;
  then <*x*>^<*y*>^<*z*> ==>. (x*y)*z by A3,Def18;
  then <*x*>^<*y*z*> ==>. (x*y)*z by Lm9;
  then
A4: <*x*(y*z)*> ==>. (x*y)*z by Lm10;
  <*y*>^<*z*> ==>. y*z by A2,A3,Def18;
  then <*x*>^(<*y*>^<*z*>) ==>. x*(y*z) by A1,Def18;
  then <*x*>^<*y*>^<*z*> ==>. x*(y*z) by FINSEQ_1:32;
  then <*x*y*>^<*z*> ==>. x*(y*z) by Lm8;
  then <*x*y*z*> ==>. x*(y*z) by Lm10;
  hence thesis by A4;
end;
