%------------------------------------------------------------------------------
% File     : SEV603^1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set Theory
% Problem  : Predicate insert in Univ
% Version  : Especial.
% English  :

% Refs     :
% Source   : [TPTP]
% Names    : 001 [TPTP]

% Status   : Theorem
% Rating   : 0.00 v9.3.0
% Syntax   : Number of formulae    :    7 (   3 unt;   3 typ;   0 def)
%            Number of atoms       :   16 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :   25 (   0   ~;   1   |;   0   &;  24   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type decls  :    3 (   3 !>P;   0 !>D)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   0 con; 2-4 aty)
%            Number of variables   :   15 (   0   ^;  12   !;   0   ?;  15   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR_NDT

% Comments : Originally HOL4 Kananaskis 10
%------------------------------------------------------------------------------
thf(in,type,
    in: 
      !>[A: $tType] : ( A > ( A > $o ) > $o ) ).

thf(univ,type,
    univ: 
      !>[A: $tType] : ( A > $o ) ).

thf(insert,type,
    insert: 
      !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).

thf('pred_set/IN_INSERT_',axiom,
    ! [A: $tType,X: A,Y: A,S: A > $o] :
      ( ( in @ A @ X @ ( insert @ A @ Y @ S ) )
      = ( ( X = Y )
        | ( in @ A @ X @ S ) ) ) ).

thf('pred_set/IN_UNIV_',axiom,
    ! [A: $tType,X: A] : ( in @ A @ X @ ( univ @ A ) ) ).

thf('pred_set/EXTENSION_',axiom,
    ! [A: $tType,S: A > $o,T: A > $o] :
      ( ( S = T )
      = ( ! [X: A] :
            ( ( in @ A @ X @ S )
            = ( in @ A @ X @ T ) ) ) ) ).

thf('pred_set/INSERT_UNIV_',conjecture,
    ! [A: $tType,X: A] :
      ( ( insert @ A @ X @ ( univ @ A ) )
      = ( univ @ A ) ) ).

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