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 Th14:
  for f be Function st i in I & f = F.i holds (doms F).i = dom f
proof
A1: dom F = I by PARTFUN1:def 2;
  let f be Function;
  assume i in I & f = F.i;
  hence thesis by A1,FUNCT_6:22;
end;
