reserve I for non empty set;
reserve M for ManySortedSet of I;
reserve Y,x,y,y1,i,j for set;
reserve k for Element of NAT;
reserve p for FinSequence;
reserve S for non void non empty ManySortedSign;
reserve A for non-empty MSAlgebra over S;

theorem
  for C be Element of EqRelLatt the Sorts of A st C is MSCongruence of A
  holds CongrCl C = C
proof
  let C be Element of EqRelLatt the Sorts of A;
  set Z = {x where x is Element of EqRelLatt the Sorts of A : x is
  MSCongruence of A & C [= x};
  now
    let q be Element of EqRelLatt the Sorts of A;
    assume q in Z;
    then ex x be Element of EqRelLatt the Sorts of A st q = x & x is
    MSCongruence of A & C [= x;
    hence C [= q;
  end;
  then
A1: C is_less_than Z by LATTICE3:def 16;
  assume C is MSCongruence of A;
  then C in Z;
  hence thesis by A1,LATTICE3:41;
end;
