reserve I, G, H for set, i, x for object,
  A, B, M for ManySortedSet of I,
  sf, sg, sh for Subset-Family of I,
  v, w for Subset of I,
  F for ManySortedFunction of I;

theorem
  A in B implies A is Element of B
proof
  assume
A1: A in B;
  let i be object;
  assume i in I;
  hence thesis by A1;
end;
