
theorem Th17:
  for C being FormalContext holds (ObjectDerivation(C)).{} = the carrier' of C
proof
  let C be FormalContext;
  reconsider e = {} as Subset of the carrier of C by XBOOLE_1:2;
  set A = {a where a is Attribute of C : for o being Object of C st o in e
  holds o is-connected-with a};
A1: for x being object holds x in A implies x in the carrier' of C
  proof
    let x be object;
    assume x in A;
    then
    ex x9 being Attribute of C st x9 = x & for o being Object of C st o in
    e holds o is-connected-with x9;
    hence thesis;
  end;
A2: for x being object holds x in the carrier' of C implies x in A
  proof
    let x be object;
    assume x in the carrier' of C;
    then reconsider x as Attribute of C;
    for o being Object of C st o in e holds o is-connected-with x;
    hence thesis;
  end;
  (ObjectDerivation(C)).e = {a where a is Attribute of C : for o being
  Object of C st o in e holds o is-connected-with a} by Def2;
  hence thesis by A1,A2,TARSKI:2;
end;
