Editing Analytic proof (section)

{{Short description|Fundamental theory of logical analysis}}
In [[mathematics]], an '''analytic proof''' is a proof of a theorem in [[mathematical analysis|analysis]] that only makes use of methods from analysis, and that does not predominantly make use of algebraic or geometrical methods.  The term was first used by [[Bernard Bolzano]], who first provided a non-analytic proof of his [[intermediate value theorem]] and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic (Bolzano 1817).  

Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In [[proof theory]], an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.