In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity (0  1)  (0  1)  1. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We als...

In this Mizar article, we complete the formalization of one of the items from Abad and Abad’s challenge list of “Top 100 Theorems” about Liouville numbers and the existence of transcendental numbers. It is item #18 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http: //www.cs.ru.nl/F.Wiedijk/100/. Liouville numbers were introduced by Joseph Liouville in 1844 [15] as an ...