re - leiden university
Post on 22-Mar-2022
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RE Axis
S E B x C
TEC xD-
CLAIM : (Ros) OT = Rof Sot )T -Q
41 NOTE "I"
is EQUAliTyOTSL I
NEED "
yep ⇒ XEQyep ⇒ xefaibl Kalb) ERXEQ ⇒ XEP
.
(at A , be B)
RE A xD. * an *
RECALL Rose E A XC , ,
S E B x C Primes" (R' ,s'
)( a ,
b) C- 12*05" ⇐3 To AVOID
T E ( xD CONFUSION ,
- there exists"
a middle"
g ,
THIS HOLDS
i ALWAYSsuch that (a, g) ER & ( 9 ,b )
(l
Fg ED S -T. ( a ,HER AND ( y ,b) ES .
→
WE HAVE TO SET UP OUR SET OF" PREVIOUS KNOWLEDGE "
STATEMENTS
REAXB ,S E Bxc
,TEC xD ; ONE DIRECTION
( a ,'d) E ( Ros) OT ⇒ ( a ,
c- Ro ( Sot )#
( Ca )#
(Ca) ⇒ F y C- E ST
la,9) EROS AND ( Y
,d) ET- -
ku) (Carl
fu) -772 C- Est (a. 2) ER & ( 2,9 ) ES-
(Cme ) ( Cen )
From Kun) , Ken) ,4n) WANT %nYf,( Cl )
RECALL
(Cr) ( a ,c) t Ro ( so -11
1- I e B , faithfully (Dayton : IEEB s# DY
F STEC, ( I , 5) ES & ( 5 ,HTT (Drl (D2)EF5eC st.DKe-
Di
M .IF (Culkin) #m) HOLD THEN 9%4 AND 27-2 SATISFY
Dn'& Df so ( Dn) & (DY ARE TRUE
,AND HENCE 5015144
- ( Ss) ( 541
--
using ( YEC AND (aisle ROTS and ( g.DIET .
ZEB AND ( oh, 2) ER and (2 , 9) ES
"
- -is, ) ( 54
PROVE CD'll :( aid ER & (2.d) c- Sot ( D'll )- -
= Css) ⇒ TRUE REMAINS
(2,41 E so -1 Ig ( 2. g) ES & Ig , d) t 'T
choose g : - y ,SO THEN By (S2) 4154 )
( 2 , g) ES & ( Y,d) ET is TRUE .
So Dh IS TRUE FOR THAT 2,so D1 IS ALSO TRUE
( Ss) ( 541
NEXT WE USE [ YEC AND TEES and THET .]ZEB AND ( A, 2) ER and (2 , 9) ES
"
- -is, ) ( S4
to Prove ④ 4 :( 2 , y ) es & ( y ,dltTBut THESE ARE Exactly (S2 ) & (S4) so Dk is TRUE
,
WITH THAT CHOICE OF Y.
But THEN D2 is TRUE AS SUCH A 4 Exists .
PROVEN : laid ) t ( Ros)oT = ) (a. d) f Ro OT )
REMAINS : ( a ,d ) ERO ( 50T ) ⇒ ( a. d) C- (Ros )oTI# #
(Cal Den-
,
'
#
FYEB,Caister & ( y ,dlESoT
,(Dil f E la ,I ) C- Ros &
/ ( I , d) ET } Daz72 EC ( 9,2 ) C- S 212 , d) ET
'
Ti - l CRI 75 la , 5) ER 415,5 )ts( I cc 's , I
-
-1727172Lc's .ci ,c's ⇒ l
l TAKE 5=51 & 5--2/[Assume ciici.ci ) )
(
y c.'
⇒ Den ,ci⇒Dz2,s'
-
- InDyp remains
LASTLY : Da , ⇐ ' ( a ,2 ) C- Ros- -
⇒ F y la , g) ER & ( 9,2 )tS--
NOTE = NOTE
ca'
a'
so ci.ci ⇒ Den.
so C,
'
. . Cg'
⇒"
ALL"
D 's.
Ro§oT)=(RoS÷ NEXT : in picture.
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