Analysis of Algorithms: An Example of a Sort Algorithm

Autor: Grzegorz Bancerek
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Zdroj: Formalized Mathematics, Vol 21, Iss 1, Pp 1-23 (2013)
ISSN: 1898-9934
1426-2630
Popis: Now we state the propositions: (1) (i) 1 mod 2 = 1, and (ii) 2 mod 2 = 0. (2) Let us consider a non empty non void many sorted signature Σ, an algebra A over Σ, a subalgebra B of A, a sort symbol s of Σ, and a set a. Suppose a ∈ (the sorts of B)(s). Then a ∈ (the sorts of A)(s). (3) Let us consider a non empty set I, sets a, b, c, and an element i of I. Then c ∈ (i -singleton a)(b) if and only if b = i and c = a. (4) Let us consider a non empty set I, sets a, b, c, d, and elements i, j of I. Then c ∈ (i -singleton a ∪ j -singleton d)(b) if and only if b = i and c = a or b = j and c = d. The theorem is a consequence of (3).
Databáze: OpenAIRE