%------------------------------------------------------------------------------
% File     : SEV487^1 : TPTP v9.0.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : PAIRWISE_EMPTY
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : PAIRWISE_EMPTY_.p [Kal16]

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :    6 (   2 unt;   3 typ;   0 def)
%            Number of atoms       :   11 (   3 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   24 (   2   ~;   0   |;   2   &;  19   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-3 aty)
%            Number of variables   :   12 (   0   ^;   9   !;   0   ?;  12   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_const_const/sets/pairwise',type,
    'const/sets/pairwise': 
      !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > $o ) ).

thf('thf_const_const/sets/IN',type,
    'const/sets/IN': 
      !>[A: $tType] : ( A > ( A > $o ) > $o ) ).

thf('thf_const_const/sets/EMPTY',type,
    'const/sets/EMPTY': 
      !>[A: $tType] : ( A > $o ) ).

thf('thm/sets/NOT_IN_EMPTY_',axiom,
    ! [A: $tType,A0: A] :
      ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).

thf('thm/sets/pairwise_',axiom,
    ! [A: $tType,A0: A > $o,A1: A > A > $o] :
      ( ( 'const/sets/pairwise' @ A @ A1 @ A0 )
      = ( ! [A2: A,A3: A] :
            ( ( ( 'const/sets/IN' @ A @ A2 @ A0 )
              & ( 'const/sets/IN' @ A @ A3 @ A0 )
              & ( A2 != A3 ) )
           => ( A1 @ A2 @ A3 ) ) ) ) ).

thf('thm/sets/PAIRWISE_EMPTY_',conjecture,
    ! [A: $tType,A0: A > A > $o] :
      ( ( 'const/sets/pairwise' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
      = $true ) ).

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