## Section: New Results

### Formalization of Analysis concepts

Participants : Cyril Cohen, Damien Rouhling.

To study problems in control, we worked on the notion of compacts and showed how to express it using filters, as in Coquelicot.

We experimented with sets of notations to make computing with limits simpler. We also generalized the notion of "big enough" that can usually be found when reasoning about functions at infinity (or sequences) so that it now works with arbitrary filters. Finally, we started experimenting with a new point of view on "small o" notations.

We also started work on formalizing in Coq the Cauchy-Lipschitz theorem (also known as Picard-Lindelöf), which proves the existence and uniqueness of solutions to differential equations.

We expect all these small advances to prepare the ground for work on various aspects of robotics and control. Part of this work was published in an international conference [20].