With Alex Simpson.

**Abstract:** We present a constructive meta-theorem about sequential continuity which allows us to conclude from a constructive proof of existence of a function between complete metric spaces satisfying a given system of (functional) equations that there also exists a sequentially continuous function satisfying the system.

**Presented at:** *Trends in Constructive mathematics*, Frauenwörth am Chimsee, Germany, June 2006.

**Download slides:** continuity_begets_continuity_bavaria_slides.pdf