TPTP Problem File: SEU799^2.p
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% File : SEU799^2 : TPTP v8.2.0. Released v3.7.0.
% Domain : Set Theory
% Problem : More about Functions - Injective Functions
% Version : Especial > Reduced > Especial.
% English : (! A:i.! B:i.! f:i.in f (injFuncSet A B) -> in f (funcSet A B))
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC301l [Bro08]
% Status : Theorem
% Rating : 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% Number of atoms : 9 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 25 ( 0 ~; 0 |; 0 &; 22 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=424
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thf(in_type,type,
in: $i > $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ) ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf(injective_type,type,
injective: $i > $i > $i > $o ).
thf(injFuncSet_type,type,
injFuncSet: $i > $i > $i ).
thf(injFuncSet,definition,
( injFuncSet
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( funcSet @ A @ B )
@ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
thf(injFuncSetFuncIn,conjecture,
( dsetconstrEL
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ).
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