TPTP Problem File: CAT034+4.p
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%------------------------------------------------------------------------------
% File : CAT034+4 : TPTP v8.2.0. Released v3.4.0.
% Domain : Category Theory
% Problem : Yoneda Embedding T04
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Woj97] Wojciechowski (1997), Yoneda Embedding
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t4_yoneda_1 [Urb08]
% Status : Theorem
% Rating : 1.00 v3.4.0
% Syntax : Number of formulae : 42652 (6318 unt; 0 def)
% Number of atoms : 311629 (35033 equ)
% Maximal formula atoms : 208 ( 7 avg)
% Number of connectives : 313231 (44254 ~;3313 |;152432 &)
% (7334 <=>;105898 =>; 0 <=; 0 <~>)
% Maximal formula depth : 150 ( 8 avg)
% Maximal term depth : 12 ( 1 avg)
% Number of predicates : 2320 (2318 usr; 3 prp; 0-8 aty)
% Number of functors : 5889 (5889 usr;1246 con; 0-10 aty)
% Number of variables : 119857 (114059 !;5798 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Chainy large version: includes all preceding MML articles.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
include('Axioms/SET007/SET007+0.ax').
include('Axioms/SET007/SET007+1.ax').
include('Axioms/SET007/SET007+2.ax').
include('Axioms/SET007/SET007+3.ax').
include('Axioms/SET007/SET007+4.ax').
include('Axioms/SET007/SET007+5.ax').
include('Axioms/SET007/SET007+6.ax').
include('Axioms/SET007/SET007+7.ax').
include('Axioms/SET007/SET007+8.ax').
include('Axioms/SET007/SET007+9.ax').
include('Axioms/SET007/SET007+10.ax').
include('Axioms/SET007/SET007+11.ax').
include('Axioms/SET007/SET007+12.ax').
include('Axioms/SET007/SET007+13.ax').
include('Axioms/SET007/SET007+14.ax').
include('Axioms/SET007/SET007+15.ax').
include('Axioms/SET007/SET007+16.ax').
include('Axioms/SET007/SET007+17.ax').
include('Axioms/SET007/SET007+18.ax').
include('Axioms/SET007/SET007+19.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+21.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+23.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+25.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+27.ax').
include('Axioms/SET007/SET007+28.ax').
include('Axioms/SET007/SET007+29.ax').
include('Axioms/SET007/SET007+30.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+32.ax').
include('Axioms/SET007/SET007+33.ax').
include('Axioms/SET007/SET007+34.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+36.ax').
include('Axioms/SET007/SET007+37.ax').
include('Axioms/SET007/SET007+38.ax').
include('Axioms/SET007/SET007+39.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+41.ax').
include('Axioms/SET007/SET007+42.ax').
include('Axioms/SET007/SET007+43.ax').
include('Axioms/SET007/SET007+44.ax').
include('Axioms/SET007/SET007+45.ax').
include('Axioms/SET007/SET007+46.ax').
include('Axioms/SET007/SET007+47.ax').
include('Axioms/SET007/SET007+48.ax').
include('Axioms/SET007/SET007+49.ax').
include('Axioms/SET007/SET007+50.ax').
include('Axioms/SET007/SET007+51.ax').
include('Axioms/SET007/SET007+52.ax').
include('Axioms/SET007/SET007+53.ax').
include('Axioms/SET007/SET007+54.ax').
include('Axioms/SET007/SET007+55.ax').
include('Axioms/SET007/SET007+56.ax').
include('Axioms/SET007/SET007+57.ax').
include('Axioms/SET007/SET007+58.ax').
include('Axioms/SET007/SET007+59.ax').
include('Axioms/SET007/SET007+60.ax').
include('Axioms/SET007/SET007+61.ax').
include('Axioms/SET007/SET007+62.ax').
include('Axioms/SET007/SET007+63.ax').
include('Axioms/SET007/SET007+64.ax').
include('Axioms/SET007/SET007+65.ax').
include('Axioms/SET007/SET007+66.ax').
include('Axioms/SET007/SET007+67.ax').
include('Axioms/SET007/SET007+68.ax').
include('Axioms/SET007/SET007+69.ax').
include('Axioms/SET007/SET007+70.ax').
include('Axioms/SET007/SET007+71.ax').
include('Axioms/SET007/SET007+72.ax').
include('Axioms/SET007/SET007+73.ax').
include('Axioms/SET007/SET007+74.ax').
include('Axioms/SET007/SET007+75.ax').
include('Axioms/SET007/SET007+76.ax').
include('Axioms/SET007/SET007+77.ax').
include('Axioms/SET007/SET007+78.ax').
include('Axioms/SET007/SET007+79.ax').
include('Axioms/SET007/SET007+80.ax').
include('Axioms/SET007/SET007+81.ax').
include('Axioms/SET007/SET007+82.ax').
include('Axioms/SET007/SET007+83.ax').
include('Axioms/SET007/SET007+84.ax').
include('Axioms/SET007/SET007+85.ax').
include('Axioms/SET007/SET007+86.ax').
include('Axioms/SET007/SET007+87.ax').
include('Axioms/SET007/SET007+88.ax').
include('Axioms/SET007/SET007+89.ax').
include('Axioms/SET007/SET007+90.ax').
include('Axioms/SET007/SET007+91.ax').
include('Axioms/SET007/SET007+92.ax').
include('Axioms/SET007/SET007+93.ax').
include('Axioms/SET007/SET007+94.ax').
include('Axioms/SET007/SET007+95.ax').
include('Axioms/SET007/SET007+96.ax').
include('Axioms/SET007/SET007+97.ax').
include('Axioms/SET007/SET007+98.ax').
include('Axioms/SET007/SET007+99.ax').
include('Axioms/SET007/SET007+100.ax').
include('Axioms/SET007/SET007+101.ax').
include('Axioms/SET007/SET007+102.ax').
include('Axioms/SET007/SET007+103.ax').
include('Axioms/SET007/SET007+104.ax').
include('Axioms/SET007/SET007+105.ax').
include('Axioms/SET007/SET007+106.ax').
include('Axioms/SET007/SET007+107.ax').
include('Axioms/SET007/SET007+108.ax').
include('Axioms/SET007/SET007+109.ax').
include('Axioms/SET007/SET007+110.ax').
include('Axioms/SET007/SET007+111.ax').
include('Axioms/SET007/SET007+112.ax').
include('Axioms/SET007/SET007+113.ax').
include('Axioms/SET007/SET007+114.ax').
include('Axioms/SET007/SET007+115.ax').
include('Axioms/SET007/SET007+116.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+118.ax').
include('Axioms/SET007/SET007+119.ax').
include('Axioms/SET007/SET007+120.ax').
include('Axioms/SET007/SET007+121.ax').
include('Axioms/SET007/SET007+122.ax').
include('Axioms/SET007/SET007+123.ax').
include('Axioms/SET007/SET007+124.ax').
include('Axioms/SET007/SET007+125.ax').
include('Axioms/SET007/SET007+126.ax').
include('Axioms/SET007/SET007+127.ax').
include('Axioms/SET007/SET007+128.ax').
include('Axioms/SET007/SET007+129.ax').
include('Axioms/SET007/SET007+130.ax').
include('Axioms/SET007/SET007+131.ax').
include('Axioms/SET007/SET007+132.ax').
include('Axioms/SET007/SET007+133.ax').
include('Axioms/SET007/SET007+134.ax').
include('Axioms/SET007/SET007+135.ax').
include('Axioms/SET007/SET007+136.ax').
include('Axioms/SET007/SET007+137.ax').
include('Axioms/SET007/SET007+138.ax').
include('Axioms/SET007/SET007+139.ax').
include('Axioms/SET007/SET007+140.ax').
include('Axioms/SET007/SET007+141.ax').
include('Axioms/SET007/SET007+142.ax').
include('Axioms/SET007/SET007+143.ax').
include('Axioms/SET007/SET007+144.ax').
include('Axioms/SET007/SET007+145.ax').
include('Axioms/SET007/SET007+146.ax').
include('Axioms/SET007/SET007+147.ax').
include('Axioms/SET007/SET007+148.ax').
include('Axioms/SET007/SET007+149.ax').
include('Axioms/SET007/SET007+150.ax').
include('Axioms/SET007/SET007+151.ax').
include('Axioms/SET007/SET007+152.ax').
include('Axioms/SET007/SET007+153.ax').
include('Axioms/SET007/SET007+154.ax').
include('Axioms/SET007/SET007+155.ax').
include('Axioms/SET007/SET007+156.ax').
include('Axioms/SET007/SET007+157.ax').
include('Axioms/SET007/SET007+158.ax').
include('Axioms/SET007/SET007+159.ax').
include('Axioms/SET007/SET007+160.ax').
include('Axioms/SET007/SET007+161.ax').
include('Axioms/SET007/SET007+162.ax').
include('Axioms/SET007/SET007+163.ax').
include('Axioms/SET007/SET007+164.ax').
include('Axioms/SET007/SET007+165.ax').
include('Axioms/SET007/SET007+166.ax').
include('Axioms/SET007/SET007+167.ax').
include('Axioms/SET007/SET007+168.ax').
include('Axioms/SET007/SET007+169.ax').
include('Axioms/SET007/SET007+170.ax').
include('Axioms/SET007/SET007+171.ax').
include('Axioms/SET007/SET007+172.ax').
include('Axioms/SET007/SET007+173.ax').
include('Axioms/SET007/SET007+174.ax').
include('Axioms/SET007/SET007+175.ax').
include('Axioms/SET007/SET007+176.ax').
include('Axioms/SET007/SET007+177.ax').
include('Axioms/SET007/SET007+178.ax').
include('Axioms/SET007/SET007+179.ax').
include('Axioms/SET007/SET007+180.ax').
include('Axioms/SET007/SET007+181.ax').
include('Axioms/SET007/SET007+182.ax').
include('Axioms/SET007/SET007+183.ax').
include('Axioms/SET007/SET007+184.ax').
include('Axioms/SET007/SET007+185.ax').
include('Axioms/SET007/SET007+186.ax').
include('Axioms/SET007/SET007+187.ax').
include('Axioms/SET007/SET007+188.ax').
include('Axioms/SET007/SET007+189.ax').
include('Axioms/SET007/SET007+190.ax').
include('Axioms/SET007/SET007+191.ax').
include('Axioms/SET007/SET007+192.ax').
include('Axioms/SET007/SET007+193.ax').
include('Axioms/SET007/SET007+194.ax').
include('Axioms/SET007/SET007+195.ax').
include('Axioms/SET007/SET007+196.ax').
include('Axioms/SET007/SET007+197.ax').
include('Axioms/SET007/SET007+198.ax').
include('Axioms/SET007/SET007+199.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+201.ax').
include('Axioms/SET007/SET007+202.ax').
include('Axioms/SET007/SET007+203.ax').
include('Axioms/SET007/SET007+204.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+207.ax').
include('Axioms/SET007/SET007+208.ax').
include('Axioms/SET007/SET007+209.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+211.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+214.ax').
include('Axioms/SET007/SET007+215.ax').
include('Axioms/SET007/SET007+216.ax').
include('Axioms/SET007/SET007+217.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+219.ax').
include('Axioms/SET007/SET007+220.ax').
include('Axioms/SET007/SET007+221.ax').
include('Axioms/SET007/SET007+222.ax').
include('Axioms/SET007/SET007+223.ax').
include('Axioms/SET007/SET007+224.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+226.ax').
include('Axioms/SET007/SET007+227.ax').
include('Axioms/SET007/SET007+228.ax').
include('Axioms/SET007/SET007+229.ax').
include('Axioms/SET007/SET007+230.ax').
include('Axioms/SET007/SET007+231.ax').
include('Axioms/SET007/SET007+232.ax').
include('Axioms/SET007/SET007+233.ax').
include('Axioms/SET007/SET007+234.ax').
include('Axioms/SET007/SET007+235.ax').
include('Axioms/SET007/SET007+236.ax').
include('Axioms/SET007/SET007+237.ax').
include('Axioms/SET007/SET007+238.ax').
include('Axioms/SET007/SET007+239.ax').
include('Axioms/SET007/SET007+240.ax').
include('Axioms/SET007/SET007+241.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+243.ax').
include('Axioms/SET007/SET007+244.ax').
include('Axioms/SET007/SET007+245.ax').
include('Axioms/SET007/SET007+246.ax').
include('Axioms/SET007/SET007+247.ax').
include('Axioms/SET007/SET007+248.ax').
include('Axioms/SET007/SET007+249.ax').
include('Axioms/SET007/SET007+250.ax').
include('Axioms/SET007/SET007+251.ax').
include('Axioms/SET007/SET007+252.ax').
include('Axioms/SET007/SET007+253.ax').
include('Axioms/SET007/SET007+254.ax').
include('Axioms/SET007/SET007+255.ax').
include('Axioms/SET007/SET007+256.ax').
include('Axioms/SET007/SET007+257.ax').
include('Axioms/SET007/SET007+258.ax').
include('Axioms/SET007/SET007+259.ax').
include('Axioms/SET007/SET007+260.ax').
include('Axioms/SET007/SET007+261.ax').
include('Axioms/SET007/SET007+262.ax').
include('Axioms/SET007/SET007+263.ax').
include('Axioms/SET007/SET007+264.ax').
include('Axioms/SET007/SET007+265.ax').
include('Axioms/SET007/SET007+266.ax').
include('Axioms/SET007/SET007+267.ax').
include('Axioms/SET007/SET007+268.ax').
include('Axioms/SET007/SET007+269.ax').
include('Axioms/SET007/SET007+270.ax').
include('Axioms/SET007/SET007+271.ax').
include('Axioms/SET007/SET007+272.ax').
include('Axioms/SET007/SET007+273.ax').
include('Axioms/SET007/SET007+274.ax').
include('Axioms/SET007/SET007+275.ax').
include('Axioms/SET007/SET007+276.ax').
include('Axioms/SET007/SET007+277.ax').
include('Axioms/SET007/SET007+278.ax').
include('Axioms/SET007/SET007+279.ax').
include('Axioms/SET007/SET007+280.ax').
include('Axioms/SET007/SET007+281.ax').
include('Axioms/SET007/SET007+282.ax').
include('Axioms/SET007/SET007+283.ax').
include('Axioms/SET007/SET007+284.ax').
include('Axioms/SET007/SET007+285.ax').
include('Axioms/SET007/SET007+286.ax').
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include('Axioms/SET007/SET007+288.ax').
include('Axioms/SET007/SET007+289.ax').
include('Axioms/SET007/SET007+290.ax').
include('Axioms/SET007/SET007+291.ax').
include('Axioms/SET007/SET007+292.ax').
include('Axioms/SET007/SET007+293.ax').
include('Axioms/SET007/SET007+294.ax').
include('Axioms/SET007/SET007+295.ax').
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include('Axioms/SET007/SET007+297.ax').
include('Axioms/SET007/SET007+298.ax').
include('Axioms/SET007/SET007+299.ax').
include('Axioms/SET007/SET007+300.ax').
include('Axioms/SET007/SET007+301.ax').
include('Axioms/SET007/SET007+302.ax').
include('Axioms/SET007/SET007+303.ax').
include('Axioms/SET007/SET007+304.ax').
include('Axioms/SET007/SET007+305.ax').
include('Axioms/SET007/SET007+306.ax').
include('Axioms/SET007/SET007+307.ax').
include('Axioms/SET007/SET007+308.ax').
include('Axioms/SET007/SET007+309.ax').
include('Axioms/SET007/SET007+310.ax').
include('Axioms/SET007/SET007+311.ax').
include('Axioms/SET007/SET007+312.ax').
include('Axioms/SET007/SET007+313.ax').
include('Axioms/SET007/SET007+314.ax').
include('Axioms/SET007/SET007+315.ax').
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include('Axioms/SET007/SET007+318.ax').
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include('Axioms/SET007/SET007+321.ax').
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include('Axioms/SET007/SET007+397.ax').
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include('Axioms/SET007/SET007+425.ax').
include('Axioms/SET007/SET007+426.ax').
include('Axioms/SET007/SET007+427.ax').
include('Axioms/SET007/SET007+428.ax').
include('Axioms/SET007/SET007+429.ax').
include('Axioms/SET007/SET007+430.ax').
include('Axioms/SET007/SET007+431.ax').
include('Axioms/SET007/SET007+432.ax').
include('Axioms/SET007/SET007+433.ax').
include('Axioms/SET007/SET007+434.ax').
include('Axioms/SET007/SET007+435.ax').
include('Axioms/SET007/SET007+436.ax').
include('Axioms/SET007/SET007+437.ax').
include('Axioms/SET007/SET007+438.ax').
include('Axioms/SET007/SET007+439.ax').
include('Axioms/SET007/SET007+440.ax').
include('Axioms/SET007/SET007+441.ax').
include('Axioms/SET007/SET007+442.ax').
include('Axioms/SET007/SET007+443.ax').
include('Axioms/SET007/SET007+444.ax').
include('Axioms/SET007/SET007+445.ax').
include('Axioms/SET007/SET007+446.ax').
include('Axioms/SET007/SET007+447.ax').
include('Axioms/SET007/SET007+448.ax').
include('Axioms/SET007/SET007+449.ax').
include('Axioms/SET007/SET007+450.ax').
include('Axioms/SET007/SET007+451.ax').
include('Axioms/SET007/SET007+452.ax').
include('Axioms/SET007/SET007+453.ax').
include('Axioms/SET007/SET007+454.ax').
include('Axioms/SET007/SET007+455.ax').
include('Axioms/SET007/SET007+456.ax').
include('Axioms/SET007/SET007+457.ax').
include('Axioms/SET007/SET007+458.ax').
include('Axioms/SET007/SET007+459.ax').
include('Axioms/SET007/SET007+460.ax').
include('Axioms/SET007/SET007+461.ax').
include('Axioms/SET007/SET007+462.ax').
include('Axioms/SET007/SET007+463.ax').
include('Axioms/SET007/SET007+464.ax').
include('Axioms/SET007/SET007+465.ax').
include('Axioms/SET007/SET007+466.ax').
include('Axioms/SET007/SET007+467.ax').
include('Axioms/SET007/SET007+468.ax').
include('Axioms/SET007/SET007+469.ax').
include('Axioms/SET007/SET007+470.ax').
include('Axioms/SET007/SET007+471.ax').
include('Axioms/SET007/SET007+472.ax').
include('Axioms/SET007/SET007+473.ax').
include('Axioms/SET007/SET007+474.ax').
include('Axioms/SET007/SET007+475.ax').
include('Axioms/SET007/SET007+476.ax').
include('Axioms/SET007/SET007+477.ax').
include('Axioms/SET007/SET007+478.ax').
include('Axioms/SET007/SET007+479.ax').
include('Axioms/SET007/SET007+480.ax').
include('Axioms/SET007/SET007+481.ax').
include('Axioms/SET007/SET007+482.ax').
include('Axioms/SET007/SET007+483.ax').
include('Axioms/SET007/SET007+484.ax').
include('Axioms/SET007/SET007+485.ax').
include('Axioms/SET007/SET007+486.ax').
include('Axioms/SET007/SET007+487.ax').
include('Axioms/SET007/SET007+488.ax').
include('Axioms/SET007/SET007+489.ax').
include('Axioms/SET007/SET007+490.ax').
include('Axioms/SET007/SET007+491.ax').
include('Axioms/SET007/SET007+492.ax').
include('Axioms/SET007/SET007+493.ax').
include('Axioms/SET007/SET007+494.ax').
include('Axioms/SET007/SET007+495.ax').
include('Axioms/SET007/SET007+496.ax').
include('Axioms/SET007/SET007+497.ax').
include('Axioms/SET007/SET007+498.ax').
include('Axioms/SET007/SET007+499.ax').
include('Axioms/SET007/SET007+500.ax').
include('Axioms/SET007/SET007+501.ax').
include('Axioms/SET007/SET007+502.ax').
include('Axioms/SET007/SET007+503.ax').
include('Axioms/SET007/SET007+504.ax').
include('Axioms/SET007/SET007+505.ax').
include('Axioms/SET007/SET007+506.ax').
include('Axioms/SET007/SET007+507.ax').
include('Axioms/SET007/SET007+508.ax').
include('Axioms/SET007/SET007+509.ax').
include('Axioms/SET007/SET007+510.ax').
include('Axioms/SET007/SET007+511.ax').
include('Axioms/SET007/SET007+512.ax').
include('Axioms/SET007/SET007+513.ax').
%------------------------------------------------------------------------------
fof(dt_k1_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v2_cat_1(k1_yoneda_1(A))
& l1_cat_1(k1_yoneda_1(A)) ) ) ).
fof(dt_k2_yoneda_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m2_cat_1(k2_yoneda_1(A,B),A,k1_yoneda_1(A)) ) ).
fof(dt_k3_yoneda_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> m2_nattra_1(k3_yoneda_1(A,B),A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))) ) ).
fof(dt_k4_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m1_oppcat_1(k4_yoneda_1(A),A,k12_nattra_1(A,k1_yoneda_1(A))) ) ).
fof(dt_k5_yoneda_1,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m1_oppcat_1(C,A,B)
& m1_subset_1(D,u1_cat_1(A)) )
=> m1_subset_1(k5_yoneda_1(A,B,C,D),u1_cat_1(B)) ) ).
fof(d1_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)) ) ).
fof(t1_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k1_yoneda_1(A)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k1_yoneda_1(A)))
=> ( ( k3_cat_1(k1_yoneda_1(A),D) = k2_cat_1(k1_yoneda_1(A),E)
& k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),D),k3_cat_1(k1_yoneda_1(A),D)),B) = D
& k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),E),k3_cat_1(k1_yoneda_1(A),E)),C) = E )
=> k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),D),k3_cat_1(k1_yoneda_1(A),E)),k5_relat_1(B,C)) = k4_cat_1(k1_yoneda_1(A),D,E) ) ) ) ) ) ) ).
fof(t2_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)) ) ) ).
fof(d2_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k2_yoneda_1(A,B) = k20_ens_1(A,B) ) ) ).
fof(t3_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> r2_nattra_1(A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))) ) ) ).
fof(d3_yoneda_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m2_nattra_1(C,A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B)))
=> ( C = k3_yoneda_1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k5_nattra_1(A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B)),C,D) = k4_tarski(k4_tarski(k6_cat_1(A,k3_cat_1(A,B),D),k6_cat_1(A,k2_cat_1(A,B),D)),k22_ens_1(A,B,k10_cat_1(A,D))) ) ) ) ) ) ).
fof(t4_yoneda_1,conjecture,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))),k3_yoneda_1(A,B)),u2_cat_1(k12_nattra_1(A,k1_yoneda_1(A)))) ) ) ).
%------------------------------------------------------------------------------