Using Animation in Diagrammatic Theorem Proving

Diagrams have many uses in mathematics, one of the most ambitious of which is as a form of proof. The domain we consider is real analysis, where quanti cation issues are subtle but crucial. Computers o er new possibilities in diagrammatic reasoning, one of which is animation. Here we develop animated rules as a solution to problems of quanti cation. We show a simple application of this to constraint diagrams, and also how it can deal with the more complex questions of quanti cation and generalisation in diagrams that use more speci c representations. This allows us to tackle diÆcult theorems that previously could only be proved algebraically.