%------------------------------------------------------------------------------
% File     : QUA011^1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Quantales
% Problem  : 0 annihilates arbitrary sums from the right
% Version  : [Hoe09] axioms.
% English  :

% Refs     : [Con71] Conway (1971), Regular Algebra and Finite Machines
%          : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% Source   : [Hoe09]
% Names    : QUA11 [Hoe09] 

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0
% Syntax   : Number of formulae    :   27 (  14 unt;  12 typ;   7 def)
%            Number of atoms       :   52 (  18 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   46 (   0   ~;   1   |;   4   &;  40   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   28 (  15   ^;   9   !;   4   ?;  28   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----Include axioms for Quantales
include('Axioms/QUA001^0.ax').
%------------------------------------------------------------------------------
thf(multiplication_anni,conjecture,
    ! [X: $i > $o] :
      ( ( multiplication @ ( sup @ X ) @ zero )
      = zero ) ).

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