reserve x, y for object, I for set,
  A, B, X, Y for ManySortedSet of I;

theorem :: ZFMISC_1:31
  union (I --> {x}) = I --> x
proof
  now
    let i be object;
    assume
A1: i in I;
    hence (union (I --> {x})).i = union ((I --> {x}).i) by Def2
      .= union {x} by A1,FUNCOP_1:7
      .= x by ZFMISC_1:25
      .= (I --> x).i by A1,FUNCOP_1:7;
  end;
  hence thesis;
end;
