@TECHREPORT{Ruys99studiesin, author = {Mark Ruys}, title = {Studies in Mechanical Verification of Mathematical Proofs}, institution = {}, year = {1999} }

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Abstract

infinitely_many_p ri mes_exist = ([fac_divides:{x,y|el Nat}(ap2 LessEqN OneN x)->(ap2 LessEqN x y)->divides x (fac y)]([infinitely_bounded_prim es _exist:{x:el Nat}Ex(el

...interactively build by tacticals. Proof theoretical strength. Most proof development systems are based on a predefined, fixed set of logical environments. For example, Mizar (Trybulec and Blair 1985, =-=Rudnicki 1992-=-) verifies proofs based on a variant of ZermeloFraenkel set theory, and LEGO supports the Calculus of Constructions, with the option of inductive types or sigma types. Although not every mathematician...

...t class citizens. This makes it easy to hand over these objects to other people using other proof checkers. Examples of proof checkers which actually produce proofs are Coq (Dowek et al. 1993), LEGO (=-=Pollack 1994-=-) and Alf (Magnusson and NordstrÃ¶m 1994). Another advantage of using type theory for formalizing proofs is that we are encouraged to build constructive proofs only. Although this is not compulsory, co...