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 Th20:
  CongrLatt A is \/-inheriting
proof
  set E = EqRelLatt the Sorts of A;
  set C = CongrLatt A;
  now
    let B be Subset of C;
    reconsider d = "\/" (B,E) as MSCongruence of A by Th18;
    d in the carrier of C by MSUALG_5:def 6;
    hence "\/" (B,E) in the carrier of C;
  end;
  hence thesis by MSUALG_7:def 3;
end;
