The Seventeen Provers of the World: Foreword by Dana S. by Freek Wiedijk (auth.), Freek Wiedijk (eds.)

By Freek Wiedijk (auth.), Freek Wiedijk (eds.)

Commemorating the fiftieth anniversary of the 1st time a mathematical theorem was once confirmed by means of a working laptop or computer method, Freek Wiedijk initiated the current publication in 2004 by way of inviting formalizations of an evidence of the irrationality of the sq. root of 2 from scientists utilizing numerous theorem proving platforms.

The 17 structures incorporated during this quantity are one of the such a lot suitable ones for the formalization of arithmetic. The platforms are showcased through presentation of the formalized evidence and an outline within the kind of solutions to a regular questionnaire. The 17 structures provided are HOL, Mizar, PVS, Coq, Otter/Ivy, Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Leog, Nuprl, Omega, B approach, and Minlog.

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It is the Mizar script, as prepared by the author and checked by the system. What needs to be explained about this specific proof ? The actual proof in Mizar would now be as follows: sqtr 2 is irrational by IRRAT_1:1, INT_2:44; The presented proof is an adjusted version of the proof that the square root of any prime number is irrational (IRRAT_1:1). So, this is what the proof would have looked like if Freek Wiedijk had not submitted the IRRAT_1 article to the MML in 1999. com>. html> In particular the definition of sqrt below comes from this library.

Rational? 4 System What is the home page of the system? com/> What are the books about the system? html> What is the logic of the system? PVS is based on classical higher-order logic. What is the implementation architecture of the system? PVS is written primarily in Common Lisp. What does working with the system look like? The user interface is built on Emacs. The user normally creates specification files, typechecks them, and proves formulas interactively. There are a large number of commands for proofchain analysis, browsing, and specification and proof development and maintenance.

N = 0 ∧ |x | = real (m::nat) / real (n::nat)} Main theorem The square root of any prime number (including 2 ) is irrational. : natify-eqE simp add : not-lt-iff-le prime-into-nat mult-le-cancel-le1 ) apply (simp add : prime-def ) apply (blast dest: lt-trans1 ) done lemma rearrange: j #∗ (p#∗j ) = k #∗k =⇒ k #∗k = p#∗(j #∗j ) by (simp add : mult-ac) 45 46 Markus Wenzel and Larry Paulson lemma prime-not-square: [[m ∈ nat; p ∈ prime]] =⇒ ∀ k ∈ nat. 6 System What is the home page of the system? de> (Munich).

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