reserve x,y for set;

theorem Th14:
  for I,J being set for A being ManySortedSet of I, B being
  ManySortedSet of J holds Intersect(A, B) is ManySortedSet of I /\ J
proof
  let I,J be set, A be ManySortedSet of I, B be ManySortedSet of J;
  dom A = I & dom B = J by PARTFUN1:def 2;
  then dom Intersect(A,B) = I /\ J by Def2;
  hence thesis by PARTFUN1:def 2,RELAT_1:def 18;
end;
