Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTION E]

SECTION E]ON THE EQUI-FACTOR RELATION63

635

Dent.
F. *92-143. ) F: Hp.S8e Potid'P. ). UI'S =EGPP
[lip]. D'1R CC['S.
[*37-32] ). (l'(S IRI T) T"C1'R (1
F. (1). )F: Hp. SePotid'P. TePotid'Q. D. 1'(S 1R T) =[P'CB'Q. (2)
[*93-32] D. (1'(S 1? Tj) E geriQ (3)
F. (:3). *95-22. ) F: Hp. ). (1"(P*Q)'R C gen'Q (4)
F. (2). *95-221. *93-32. ) F: Hp.. gen'Q C G"(P*Q)'-R (5)
F.- (4). (5). ) F. Prop
*95-601. F:(IRCD)'Q.(t'QCD'Q.D'R?=B'P.PECls-+l.I.).
D"(P*)IR gencp
[Proof as in *95-6]
*95-61. F:P,Q,R~el-+1~-.D'PC(I'P.(l'QCD'Q. D'l=B'P.(l'R=B'Q.).
~'(P*Q)'R el I-+ 1. D'Y(P*Q)'Rf = s'gen'P. (1',~'(11*Q)'R = s'gen'Q
[*95-52-6601. *41[43-44]
*95-62. F: Hp *9.561. ). sgenl'P SDm sgeiiQ [*95-61.*73-2]
*95-63. F::13, QEI --- ),.(['PC 'F)P.(l'IQCI)'Q.B'PsmB'Q.:).
s'gen.'P snm s'gen'Q
Deni.
F.*9532 —)F:PQ~ke ---f.(tPCDI)'P.(t1QCI)'Q.
F. (1). *1011P23-35. *731I. ) F. Prop
956.F:P,Qel-*1l.I'PCD'P.C1'QCD'Q.B3PsnmB'Q.
p}AI"Pot'P =A. p'(1"Pot'Q = A. D. 1)'P sm. D'Q
[*95-63. *93-274. *33-181]
*95-65. F:P,Qel-*1I.(TPCD'P.PTQCD'Q.B'PsmiB'Q.
GCP =)i)*"KiP. G'Q =Q*B"BQ. D. C'P sm C'rQ
[*95-63. *93-36]
The -following example may illustrate the scope of *95-65. Let R, S be
the generating relations of two well-ordered series, neither of which has
a last term. Put P=R_ -- 2* Q =S_!Y2. Then Pis the relation of immediately preceding in the B-series, and Q is the relation of immediately
preceding in the S-series. We shall have.P, QelI -*1,. (T'P C DVP. U'Q C D'Q.