theory-generalize

To generalize a mathematical theorem, provide the proven result, its assumptions, and a proof sketch. The analysis identifies feasible generalizations across axes like higher dimensions, different norms, and weaker assumptions, detailing expected proof changes and breaking steps.

Assessing feasibility for generalizing a proof involves providing the original theorem and assumptions to analyze which proof steps would break under weaker assumptions, yielding a structured report on expected proof changes and a recommended generalization direction.

Yes, you can analyze stochastic versions by inputting the proven lemma and its proof sketch. The system articulates generalized extensions across axis variations and identifies exactly which steps of your existing proof will break under the stochastic transformation.

You do not need a complete formal proof, but you must input a proven theorem with its assumptions and a proof sketch. This input is required to generate the structured generalization analysis detailing feasible extensions and expected proof modifications across axes.

To identify breaking proof steps when extending a result to a stochastic version, input the proven theorem and its proof sketch. The analysis assesses the feasibility of the stochastic generalization and explicitly maps out the expected proof changes and failures.

After identifying the most promising generalization direction for a theorem, you should decompose the generalized proof into manageable steps. The analysis recommends a generalization direction and chains directly to the next skill for theory decomposition.