the security of cryptographic systems by using the Mizar proof checker.

conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools such as proof editors and proof checkers

The majority of work carried out in the formal methods community throughout the last three decades has (for good reasons) been devoted to special languages designed to make it easier to experiment with mechanized formal methods such as theorem provers, proof checkers and model checkers

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

This paper provides a detailed description of the automatic theorem prover Simplify, which is the proof engine of the Extended Static Checkers ESC/Java and ESC/Modula-3. Simplify uses the Nelson-Oppen method to combine decision procedures for several important theories, and also employs a matcher

Abstract. The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a

The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also di#ers in many other respects from most current systems. John Harrison has shown that one can have a Mizar mode

probabilistic interactive proof, to the design of program checkers for group theoretic computations. Two strucural theorems are proven here. One is a characterization of problems that can be checked. The other theorem establishes equivalence classes of problems such that whenever one problem in a class

This paper is organized as follows: We begin in Section 2 by describing how we use Mizar-MSE in teaching elementary logic. This is somewhat independent of the formalism used in a proof checker. Some observations collected over the years of using Mizar-MSE in teaching are in Section 3. We close

A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],-calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published