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The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
Abstract

Cited by 688 (73 self)
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. The scheme Ind concerns a unary predicate P, and states that: For every natural number k holdsP[k] provided the parameters satisfy the following conditions: • P[0], and • For every natural number k such thatP[k] holdsP[k+1]. The scheme Nat Ind concerns a unary predicateP, and states that: For every natural
Weights of Continuous Lattices 1
"... terminology for this paper. In this article we present several logical schemes. The scheme UparrowUnion deals with a relational structureA and a unary predicateP, and states that: For every family S of subsets ofA such that S = {X;X ranges over subsets ofA: P[X]} holds ↑ � S = � {↑X;X ranges over ..."
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terminology for this paper. In this article we present several logical schemes. The scheme UparrowUnion deals with a relational structureA and a unary predicateP, and states that: For every family S of subsets ofA such that S = {X;X ranges over subsets ofA: P[X]} holds ↑ � S = � {↑X;X ranges over
Association of Mizar Users
"... The article [1] provides the notation and terminology for this paper. In this paper X, Y, Z, x are sets. The scheme Separation deals with a setA and a unary predicateP, and states that: There exists a set X such that for every set x holds x ∈ X iff x ∈A andP[x] for all values of the parameters. The ..."
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The article [1] provides the notation and terminology for this paper. In this paper X, Y, Z, x are sets. The scheme Separation deals with a setA and a unary predicateP, and states that: There exists a set X such that for every set x holds x ∈ X iff x ∈A andP[x] for all values of the parameters