%------------------------------------------------------------------------------
% File     : SEU812^2 : TPTP v9.1.0. Released v3.7.0.
% Domain   : Set Theory
% Problem  : Transitive Sets
% Version  : Especial > Reduced > Especial.
% English  : (! X:i.transitiveset X -> (! A:i.in A X -> subset A X))

% Refs     : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source   : [Bro08]
% Names    : ZFC314l [Bro08]

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% Syntax   : Number of formulae    :    5 (   1 unt;   3 typ;   1 def)
%            Number of atoms       :    7 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   12 (   0   ~;   0   |;   0   &;   9   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    4 (   1   ^;   3   !;   0   ?;   4   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : http://mathgate.info/detsetitem.php?id=500
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(transitiveset_type,type,
    transitiveset: $i > $o ).

thf(transitiveset,definition,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [X: $i] :
          ( ( in @ X @ A )
         => ( subset @ X @ A ) ) ) ) ).

thf(transitivesetOp1,conjecture,
    ! [X: $i] :
      ( ( transitiveset @ X )
     => ! [A: $i] :
          ( ( in @ A @ X )
         => ( subset @ A @ X ) ) ) ).

%------------------------------------------------------------------------------