reserve I,X,x,d,i for set;
reserve M for ManySortedSet of I;
reserve EqR1,EqR2 for Equivalence_Relation of X;
reserve I for non empty set;
reserve M for ManySortedSet of I;
reserve EqR,EqR1,EqR2,EqR3,EqR4 for Equivalence_Relation of M;

theorem Th10:
  for EqR be Equivalence_Relation of M st EqR = EqR1 (/\) EqR2 holds
  EqR1 "\/" EqR = EqR1
proof
A1: EqR1 = EqR1 (\/) (EqR1 (/\) EqR2) by PBOOLE:31;
A2: for EqR4 st EqR1 (\/) (EqR1 (/\) EqR2) c= EqR4 holds EqR1 c= EqR4
     by PBOOLE:31;
  let EqR be Equivalence_Relation of M;
  assume EqR = EqR1 (/\) EqR2;
  hence thesis by A1,A2,Th6;
end;
