reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     ::ENUMSET1:41
  {A} (\/) {B} = {A,B}
proof
  now
    let i be object;
    assume
A1: i in I;
    hence ({A} (\/) {B}).i = {A}.i \/ {B}.i by PBOOLE:def 4
      .= {A}.i \/ {B.i} by A1,Def1
      .= {A.i} \/ {B.i} by A1,Def1
      .= {A.i,B.i} by ENUMSET1:1
      .= {A,B}.i by A1,Def2;
  end;
  hence thesis;
end;
