## TPTP Problem File: SEV494^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV494^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : NUMSEG_REC
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :   12 (   0 unit;   9 type;   0 defn)
%            Number of atoms       :   41 (   3 equality;  16 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   32 (   0   ~;   0   |;   0   &;  30   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :    6 (   0 sgn;   5   !;   0   ?;   0   ^)
%                                         (   6   :;   1  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

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

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

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

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

thf('thf_const_const/nums/BIT1',type,(
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' )).

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

thf('thf_const_const/iterate/..',type,(
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > \$o )).

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

thf('thf_const_const/arith/<=',type,(
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > \$o )).

thf('thm/arith/SUC_SUB1_',axiom,(
! [A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= A ) )).

thf('thm/iterate/NUMSEG_RREC_',axiom,(
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ A0 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ A0 @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ A0 ) ) ) )).

thf('thm/iterate/NUMSEG_REC_',conjecture,(
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ A0 ) )
=> ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ A0 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ A0 ) @ ( 'const/iterate/..' @ A @ A0 ) ) ) ) )).

%------------------------------------------------------------------------------
```