reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;

theorem Th11:
  o is idempotent implies (o,D).:A is idempotent
proof
  assume
A1: o is idempotent;
  let f be Element of Funcs(A,D);
  thus ((o,D).:A).(f,f) = o.:(f,f) by Def2
    .= f by A1,Th6;
end;
