Dependent Type System with Subtyping (I)Type Level Transitivity Elimination

Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also called An). λP≤ has nice meta-theoretic properties includingsubject reduction and decidability. In this article, v,e give a reformulation of λP≤ t called λII≤.The advantages of λII< include: type level transitivity elimination property and pretypesbasedsubtyping system. These features considerably fa…