Summary This article generalizes the differential method on intervals, using Mizar system [2], [3], [12]. Differentiation of real one-variable functions is introduced in [13], along standard lines (for interesting survey formalizations analysis various proof-assistants like ACL2 [11], Isabelle/HOL [10], Coq [4], see [5]), but differentiable interval restricted to open intervals. However, when c...

Interval parking functions (IPFs) are a generalization of ordinary in which each car is willing to park only fixed interval spaces. Each function can be expressed as pair (a,b), where and b dual function. We say that permutations (x,y) reachable if there an IPF (a,b) such x,y the outcomes a,b, respectively, functions. Reachability reflexive antisymmetric, but not general transitive. prove its t...