
theorem Th6:
  for I being non empty set for A being non-Empty
  TopStruct-yielding ManySortedSet of I for p being Point of Segre_Product A
  holds p is Element of Carrier A
proof
  let I be non empty set;
  let A be non-Empty TopStruct-yielding ManySortedSet of I;
  let p be Point of Segre_Product A;
  Segre_Product A = TopStruct(#product Carrier A, Segre_Blocks A#) by
PENCIL_1:def 23;
  then consider f being Function such that
A1: f=p and
A2: dom f = dom Carrier A and
A3: for x being object st x in dom Carrier A holds f.x in (Carrier A).x by
CARD_3:def 5;
A4: dom f = I by A2,PARTFUN1:def 2;
  then reconsider f as ManySortedSet of I by PARTFUN1:def 2,RELAT_1:def 18;
  for i being object st i in I holds f.i is Element of (Carrier A).i
    by A2,A3,A4;
  hence thesis by A1,PBOOLE:def 14;
end;
