TPTP Problem File: ANA119^1.p
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% File : ANA119^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : REAL_SUB_POW_L1
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : REAL_SUB_POW_L1_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 18 ( 2 unt; 14 typ; 0 def)
% Number of atoms : 8 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 73 ( 0 ~; 0 |; 0 &; 71 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 11 ( 2 ^; 8 !; 0 ?; 11 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/realax/real',type,
'type/realax/real': $tType ).
thf('thf_type_type/nums/num',type,
'type/nums/num': $tType ).
thf('thf_const_const/realax/real_sub',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/realax/real_pow',type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf('thf_const_const/realax/real_of_num',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('thf_const_const/realax/real_neg',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/realax/real_mul',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
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/sum',type,
'const/iterate/sum':
!>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
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/calc_int/REAL_MUL_LNEG_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
thf('thm/iterate/REAL_SUB_POW_R1_',axiom,
! [A: 'type/realax/real',A0: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
thf('thm/realarith/REAL_NEG_SUB_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ A0 ) )
= ( 'const/realax/real_sub' @ A0 @ A ) ) ).
thf('thm/iterate/REAL_SUB_POW_L1_',conjecture,
! [A: 'type/realax/real',A0: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ A0 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
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