Noetherian Induction

A proof technique that establishes a property for all elements of a partially ordered set that satisfies the ascending chain condition (Noetherian): assume a counterexample exists, choose a minimal counterexample with respect to the order, and derive a contradiction by reducing to strictly smaller elements.

A form of well-founded induction applicable to Noetherian partially ordered sets: to prove a property P holds for all elements, assume P holds for all strictly smaller elements and deduce P for an arbitrary element, relying on the absence of infinite strictly descending chains.