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

330

MATHEMATICAL LOGIC

[PART I

*i40'71. F. s' y" = (s'K)? = ~ y"S'
Dem.
F.*40-38. *38'31. F l. 8 y"c =? y"s'K
[*38'2] = (s'C)? y. ) F. Prop
The hypothesis R"a C a, which appears in *40-8-81, is one which plays
an important part at a later stage. In the theory of induction (Part II,
Section E) it characterizes a hereditary class, and in the theory of series it
characterizes an upper section (when combined with a C C'R).
*40-8. F:. aeKc. )a. R"aCcac: D. RCCs'K Cs'KC
Dem.
F.*37171.)::Hp. a:.aEKc. ):xea.xRy.. )XIYyEa:.
[*11-62] O. T E K. X E a. XRY.:),,, X,. Y 6 a:.
[*40-13] Da,x,y. ye S'K:
[*40-11.*10-23] D]:. ICCsK - XRY. DZ,,.y - Y 6 SCK
[*37I171] D:. Rcs'Kt C s'IK:: D)F. Prop
*40'81. F:. aeK.)a.1"aCa: ).R Cp'KCp'IK
Dem.
F.*37K171. )F::. Hp.::: a K. ): xC a. xRy D..yCa::
[Exp.Comm] ):: xRy. ):. aCK. xC a. ). yc a:.
[*2-77]:.asK. Xca:): aK.) yea (1)
F. (1). *10-11-21-27.
F::. Hp. ):: xRy. ):. aSK re. )a. x c ar: ): aSK Ic.,. ys a r:.
):. x CP'K.. Y epK::
[Imp] ):: xsp'K. x-Ry. D. yep'Kc (2)
F.(2). *37-171.F.D Prop