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

SECTION C]

INDUcriVE CARDINALS

231

*120-76. F K e6 CIS induct.- K C Cis i nd uct. ). c Cis ind uct
Dem.
F. *51-2. ) F:. a CK. )K = KC vf
[*13-12] ) e E41Ke Cis inducet.). D 4' (K v t'6a) e Cis induct (1)
F.*83-41.*1 14-301.)DF:a - C K.)E-A'(K U 'a),Sn61n4'K Xa (2)
F.(2). *120-214.:) F:.acO)E K.)
v'4t t'a) e Cis induct..e4'Kl x a 6 Cis induct (3)
E4j6K, a e Cis induct.)D. 6E1'(K U t'a) 6 CIS induct (4)
F. (1). (4). ) F: E46K, a 6 CIs induct. ). 61'f(K Ut'a) 6 Cis induct (5)
F.(5).*51-2.Syll-:)F:.KCCisinduict. ).64,'KeClsindtuct:):
K v t'a CCis induct. ). v,'( t'a) 6 CIs induct (6)
F. *83-15. *120-213. ) F. E4'A e Cls induct.
[Simp] ) F:A C CIS induct. ). ca'A e Cis induct (7)
F.(6). (7).-*120-26 )F:KcECIS induct. )
K C CIS induct. ). e,16K 6 CIS induct:.)D F. Prop
The following propositions are concerned -in establishing the converse of
*120-76 subject to a suitable hypothesis. The final outcomne is given in
*120-77.
*120-761. F: j!6,1K. E4j K E ClS indhlct. K C Cis induct
Dem.
F.*83-41. *114t301.)D F:. aECK ):,64K SMa X E6'(K - ta): 1
[*120-214] ): e,6tcK Cis induct.. at X C4'(K - t'at) CIS induct (2)
F. (2). (3). *120-721. ) F: {! 64j'K. a 6 K.D
E4A6KCE CIS induct. ). a E Cis induct (4)
F. (4). Commn. ) F. Prop
*120-762. F:KeClsinduct.A~eKc.!1AK.).(qR,S).R,S~eea'K.BA~S=A
Dern.
F *83-5.*55-201.)
FRIB S e 6,'K. B A: S = A,. x, ye a * x + y. a'' 6K.)
B VX I O, S ig4 a 664j'(KVU t'at).(BwVXJ a) A(Sv yIg4a) =A (2)
F. (1).(2). *52-41.) F:.R, S e aK. ft A S A. a{+A. ac-c 1.).
(ajP,Q).P, Q eEj'(K U t C%) PAiQ =A (3)
F.*51-16.)DF:.aA -v a e1:)D:A e(K u ta).v a!Ir% (K UL'a) (4)
F.*22.58. )F:A eKIcv a I1 nK: D: A e(1KvL'a). v. jri(Kvwt'a) (5)
F.(3).(4).(5).) F:. AE 6K.V. a! 1 n KV.v (RB, S). B, Se RK.B S=::
F.*83-15. ) F (HR, S).B,S e ej'A.BRAS =A (7)
F. (6). (7). *120-26.)F.Prop