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

494

494 ~~PROLEGOMENA TO CARDINAL ARITHMETIC [ATI

[PART 11

*74-41. F:[,PPAD'QCc.:).PIK1Q=PIQ
Dem.
I -.*33K13-131.*10-23.)D
[*4-71]: XPYYQ.Z,Y,Z. XPY.-YQZ.-yE6K:
*74-42. I-: cI'P C Q"(X. -). D'l(P Q r X) = D'PT [*37-321P401]
*74-43. -: Q""XCCU'rP. ). G'(P Qr~X) = A'~n X *37-322-401.*35-64]
*74-44. F:PIP=Q"X.:).D'(PlQr>X)=D'P.U'~(P Qrx)=C[I'QnX
[*74-42-43]
Dem.
F. *35-7. F x = (P r/3)'y.Ey 3. x = Ply (1)
F-. (1). *10-1 1281. ) F:.(ax) x = (P /3)'y. E: y/38: (qx) x-=P'y:.
[*14-204] F:. E!(P r3)'y.=-. ye/3. E!P'y (2)
F. *35.7. )F:(P r3)'y = P'y..,yE8. P'y = Ply.
[*14-28] iEy e3. E! P'y (3)
F. (2). (3).:) F. Prop
Dem.
F.*32-18.*35l.:)F:.Hp.:):xPy.E-,.x(a1P)y: (1)
[*30-34] ): E!(al1P)'y. E. E! Py (2)
F. (2). (3). ) F. Prop
[Proof as in *74-51]
*74-52. F:S~)S1~~~lUSy,..tS1)S'='.!'
Dem. _
F.*37 18. )F:Hp. ).S'y CS"I3 (1
F.*371. ):Hp.).(~x). xSy. xE S",&.
[*33-131] ).y E U'(S"13) 1 SI.
[*71-16] ).E {(S-1fl,) 1SI}y (2)
F. (1). (2). *74-51. ) F. Prop