By A. S. Smogorzhevski
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J////I D = C (i) : {p,q] {p,q} fig. (233) A x i o m B7: Let kl, (232) k 2 6 B, i, m 6 Bkl p o s ( l , k i) = p o s ( m , k i) for i=I,2. Then 9 M 6 ~ such that 9 11,... M-I} 1M 6 Bkl R Bk2 i v ~ 1 + I or 1 of p o s ( l , k i) = pos(m,ki) of c o n f i g u r a t i o n s from the e x i s t e n c e possesses normal and of a "joint" Definition: C(1) Bk I Bk 2 ~-greatest configurations. there separately. exist such sequences A x i o m B7 p o s t u l a t e s sequence. A configuration a 1 = 1 I, m = 1 M and ~ 1 + 1.
6 ~I Hl 2 6 ~2 Ha that {Vn 6 B, (nil I and nAkl) above. => n ~ k 2} => The of a inverse (iii). e. c. for m i n i m a l same there properties. c. in in some (n'k') exists Hence for of k 2 are u s e d (2219) (i). of the equivalent This following sub-bodies with to trivial proofs. "copies" and p o s t u l a t e : E Pos such that subset. "~ ~ w' Then and => n { L). serve These the 6 Pos
Above (2242) A Now £ b such are two 4 ySA. r. b ~ a, a, b to the 6 a such : b ÷ a such and = antisymmetry a c b and a ^ b exist and 3 A' A yBA by definition o f ~ , BA = A a : b. the supremum parital B < A'. that hence 6 R, that = yA. The [] a v b and ordering < . Proof: Definition I. of a v b. / Consider 6 a v b = def a 6 R. v b We have that relation (2238), c(e) co = Y A6~ show that spatial c(~) v b regions. £ c(B), 6 e V B a a < By A Ha A 6 a A whenever 6 6, A 6 a. ~ B. e, But B 6 6 R exists.