We describe the library of theorems about N-dimensional Euclidean space that has been
formalized in the HOL Light prover. This formalization was started in 2005 and has been …

BACKGROUND On June 1, 2009, Air France Flight 447 from Rio de Janeiro to Paris crashed
into the Atlantic Ocean, killing all 216 passengers and 12 crew members. Prior to the …

The Kepler conjecture asserts that no packing of congruent balls in threedimensional
Euclidean space has density greater than that of the face-centered cubic packing. The …

The theory of analysis in Isabelle/HOL derives from earlier formalizations that were limited to
specific concrete types: ℝ, ℂ and ℝ n. Isabelle's new analysis theory unifies and generalizes …

We formally prove correct a C program that implements a numerical scheme for the
resolution of the one-dimensional acoustic wave equation. Such an implementation …

In this paper, we present an approach to describe uniformly iterated “big” operations, like
i=0^nf(i) or max i∈ I f (i) and to provide lemmas that encapsulate all the commonly used …

Currently published HOL formalizations of measure theory concentrate on the Lebesgue
integral and they are restricted to real-valued measures. We lift this restriction by introducing …

Hybrid systems combine discrete and continuous dynamics, which makes them attractive as
models for systems that combine computer control with physical motion. Verification is …

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently
used principal mathematical and computational tools and techniques of the geometric …

In the recent years, numerous proof systems have improved enough to be used for formally
verifying non-trivial mathematical results. They, however, have different purposes and it is …