TPTP Problem File: SEV503^1.p

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% File     : SEV503^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : NSUM_RESTRICT
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 1.00 v7.1.0
% Syntax   : Number of formulae    :    9 (   0 unit;   7 type;   0 defn)
%            Number of atoms       :   39 (   3 equality;  25 variable)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives :   31 (   0   ~;   0   |;   0   &;  28   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   13 (   0 sgn;   8   !;   0   ?;   1   ^)
%                                         (  13   :;   4  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
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thf('thf_type_type/nums/num',type,(
    'type/nums/num': $tType )).

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

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

thf('thf_const_const/nums/NUMERAL',type,(
    'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' )).

thf('thf_const_const/nums/_0',type,(
    'const/nums/_0': 'type/nums/num' )).

thf('thf_const_const/iterate/nsum',type,(
    'const/iterate/nsum': 
      !>[A: $tType] :
        ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) )).

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

thf('thm/iterate/NSUM_EQ_',axiom,(
    ! [A: $tType,A0: A > 'type/nums/num',A1: A > 'type/nums/num',A2: A > $o] :
      ( ! [A3: A] :
          ( ( 'const/sets/IN' @ A @ A3 @ A2 )
         => ( ( A0 @ A3 )
            = ( A1 @ A3 ) ) )
     => ( ( 'const/iterate/nsum' @ A @ A2 @ A0 )
        = ( 'const/iterate/nsum' @ A @ A2 @ A1 ) ) ) )).

thf('thm/iterate/NSUM_RESTRICT_',conjecture,(
    ! [A: $tType,A0: A > 'type/nums/num',A1: A > $o] :
      ( ( 'const/sets/FINITE' @ A @ A1 )
     => ( ( 'const/iterate/nsum' @ A @ A1
          @ ^ [A2: A] :
              ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ A @ A2 @ A1 ) @ ( A0 @ A2 ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
        = ( 'const/iterate/nsum' @ A @ A1 @ A0 ) ) ) )).

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