## Section: New Results

### Mathematical Components Analysis

Participants : Cyril Cohen, Damien Rouhling, Reynald Affeldt [AIST Japan] , Assia Mahboubi [Inria Gallinette] , Pierre-Yves Strub [Ecole Polytechnique] .

As a synthesis of the lessons learned in the usage of Mathematical
Components and Coquelicot, we develop an extension of the Mathematical
Components library to cover questions of analysis. This work includes
a new tactic called `near` to handle reasoning steps around limits and
filters and little-o notation (following Landau's style of asymptotic
reasoning). This work is described in [6].
There also contains a new formalization of topoligical structures, Rolle's theorem,
the intermediate value theorem, and Heine Borel's theorem. Ongoing work
concentrates on a better design of the topological hierarchy and a
simplification of the properties expected from real numbers (following
a design by A. Mahboubi and P.-Y. Strub).

Some of this work also includes experiments performed with the Lean theorem prover (developed at Microsoft Research).