188. [C. 1. e.] Proof of Taylor’s Theorem

C Proof of Theorem 4 . 1 a Proof of Theorem 3 . 1

26 2. 1 is not a proof. From the induction hypotheses we have that`MT 1 = fail. If s 0 is either an axiom or an assumption, then is apply(then(t 1 ; \t "); \s 0 ") and`MT Tac(\s 0 "). If s 0 is neither an axiom nor an assumption, then is apply(then(t 1 ; \t "); fail) with`MT Tac(fail). In both cases, from axiom (A9), the induction hypotheses and by applying ifE we havè MT = fail 25 Theorem C.1 ...

Proof of Theorem 1

Proof of Theorem 1

A new class of burst-error-correcting codes and its application to PCM tape recording systems, Proof of Theorem 1. Let j 1 < j 2 < : : : < j s be a sequence consisting of all indexes 0 < j r h such that a j 6 = a j?1 ; note that j s = r h , and deene j s+1 = j s + 1. Fix T to a value less than or equal to r v. For every 1 ` s we have,

Proof of Theorem 1

Caution: These polynomials are referred to as w0, w1, w2, ... in Sections 5-8 of [1]. However, beginning with Section 9 of [1], Hazewinkel uses the notations w1, w2, w3, ... for some different polynomials (the so-called big Witt polynomials, defined by formula (9.25) in [1]), which are not the same as our polynomials w1, w2, w3, ... (though they are related to them: in fact, the polynomial wk t...

Another proof of Banaschewski's surjection theorem

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...