Y. Elle-a-aussi-Été-utilisée-par, La preuve utilisée s'appuie sur quelques notions non élémentaires, comme le raisonnement sur les intégrales impropres ou la dérivation sous le signe d'intégration. Les intégrales généralisées étaient absentes de la bibliothèque Coquelicot à ce moment-là. Les fonctions totales ont cependant permis de simplifier les démonstrations. Ce travail a été une motivation pour formaliser les intégrales de Riemann impropres actuellement présentes dans la bibliothèque Coquelicot. La formalisation actuelle des nombres complexes permet d'utiliser les limites et les dérivées de fonctions complexes, ainsi que les intégrales de fonctions à variable réelle, De nombreuses notions spécifiques aux fonctions complexes, comme les fonctions analytiques et les intégrales de chemin, sont encore à formaliser. L'objectif serait de prouver qu'une équation différentielle linéaire d'ordre 1 à coefficients matriciels admet une unique solution holomorphe sur un ouvert étoilé

L. 'intégrale-de-kurzweil-henstock, ou intégrale de jauge) a été formalisée pendant l'été 2014 par X. Onfroy. Cette intégrale est une généralisation de l'intégrale de Riemann

Á. Pelayo, V. Voevodsky, and M. A. Warren, PVW15] ; il serait intéressant de voir dans quelle mesure il est possible de faire de l'analyse avec ces nombres. Comme il s'agit d'un anneau commutatif valué, il est a priori possible d'étendre la bibliothèque Coquelicot afin d'obtenir gratuitement des limites et des dérivées, Un autre point à étudier serait de rattacher des nombres autres que les nombres réels ou complexes à la bibliothèque Coquelicot comme les nombres p-adiques. Ces nombres ont déjà été implémentés en Coq par Pour finir, la bibliothèque Coquelicot est encore très dépendante des nombres réels de la bibliothèque standard. En particulier, les espaces uniformes en dépendent par le prédicat ball : U -> R -> U et les intégrales de Riemann sont définies pour les fonctions à variable réelle et à valeur dans un R-module

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