38 Mr Nicod, A Reduction in the number 



Theorem, P\irlQ\QIQ\P 



Dem. : Prop. -^^^-^^ -^ , r Lemma, reeult. 



p q, r s 



Hence, by Perm., P \ Q/Q, i.e. 



P I 5'/^ I s/q i P/^ (^') 



Syllogism, i? | 5*/^ I q/s \ p/s 



o s s 

 Gives _p D (/ . D : fy D s . D . jj D 6' for ^^ — 



Dem. : In this Dem., Permutation is used to correct the 

 twisting action of S\ much as handwriting has first to be inverted, 

 if it is to be seen right in a mirror. 



By 8' ~ -^ , I" Perm., and Perm., 



•^ p q, r s 



qjs I u I u I sjq {a) 



•^ p q, r s 



qjs I u I sjq I u (b) 

 By ^- i^lgA^ ^/glW^ g/HW^ ^ H^', h6, result. 



Association, p \ q/r | q \pjr 



The structure of the proof is this : 



Syll. " Il'' ' • 

 p q, r s 



gives _p I g/r . D : q/r | ?' . {p/r. 



We now need only the Lemma q \ q/r | r for our result to 

 follow by Syll. twice. 



Lemma, q \ q/p | p 



The proof of this lemma — call it L — is as follows : We prove 

 (a) q I LjL, (b) L/L \ q/q. From this, by Syll. and TautoL, the 

 result follows. 



Dem. : (a) By Syll. ^ , 

 r, s 



p\qlq-:^-q/p\plp (1) 



