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- Robert Milewski
- 2004

[21] provide the notation and terminology for this paper. 1. PRELIMINARIES The following four propositions are true: (1) Let L be an add-associative right zeroed right complementable non empty loop structure and p be a finite sequence of elements of the carrier of L. If for every natural number i such that i ∈ dom p holds p(i) = 0 L , then ∑ p = 0 L. (2)… (More)

- Robert Milewski
- 2007

the terminology and notation for this paper. The following propositions are true: (1) For all natural numbers n, m such that n = 0 and m = 0 holds (n · m − n − m) + 1 0. (2) For all real numbers x, y such that y > 0 holds min(x,y) max(x,y) 1. (3) For all real numbers x, y such that for every real number c such that c > 0 and c < 1 holds c · x y holds y 0.… (More)

- Robert Milewski
- 2004

The following propositions are true: (1) For every natural number n holds 0 − n = 0. (3) 1 Let D be a non empty set, p be a finite sequence of elements of D, and n be a natural number. If 1 ≤ n and n ≤ len p, then p = (p(n − 1)) p(n) (p n). Let us observe that every left zeroed add-right-cancelable right distributive left unital commuta-tive associative non… (More)

PURPOSE
The aim of the study was to create a predictive model of blastocyst development based on morphokinetic parameters of time-lapse embryoscope monitoring.
METHODS
Time-lapse recordings of 432 embryos (obtained from 77 patients), monitored in Embryoscope, were involved in the study. Patients underwent in vitro fertilization according to standard… (More)

– Mizar Mathematical Library (MML) [7] is a database containing more than 900 articles verified automatically by the MIZAR system making it one of the biggest databases of computer-checked mathematical knowledge in the world. The submission process of new articles, the great number of revisions and many experiments on the MML database depend on the… (More)

In the paper some notions useful in formalization of [11] are introduced, e.g. the definition of the poset of subsets of a set with inclusion as an ordering relation. Using the theory of many sorted sets authors formulate the definition of product of relational structures. The terminology and notation used in this paper are introduced in the following In… (More)

- Robert Milewski
- 2002

provide the notation and terminology for this paper. 1. PRELIMINARIES Let A be a set, let X be a set, let D be a non empty set of finite sequences of A, let p be a partial function from X to D, and let i be a set. Then p i is an element of D. We adopt the following rules: k, t, i, j, m, n denote natural numbers, x denotes a set, and D denotes a non empty… (More)

- Robert Milewski
- 1994

Let L be a non empty reflexive relational structure. The functor CompactSublatt(L) yields a strict full relational substructure of L and is defined as follows: (Def. 1) For every element x of L holds x ∈ the carrier of CompactSublatt(L) iff x is compact. Let L be a lower-bounded non empty reflexive antisymmetric relational structure. Observe that… (More)

- Robert Milewski
- 2004

The article is a Mizar formalization of [7, 168–169]. We show definition and fundamental theorems from theory of basis of continuous lattices. The terminology and notation used in this paper are introduced in the following The following proposition is true (1) For every non empty poset L and for every element x of L holds compactbelow(x) = ↓ ↓ x ∩ the… (More)