MATH.Preface:3.6 - Constituent actions in ongoing work

A symbolic rewrite can be part of proving a lemma while that lemma’s proof is part of proving a larger claim. The required domain constrains the rewrite at that same moment: cancelling a factor is permissible only under the relevant algebraic conditions, and excluding zero would change a claim that is meant to include it. Knowing the symbols and the theorem goal can leave the intermediate reasoning unavailable. Recover or obtain that reasoning rather than treat the smaller calculation as proof of the whole.

FPF B.1.5.EW helps recover these constituent–whole connections; B.1.5.RS examines a proposed replacement. Use the parts of the vertical that can change the present result. A Method described here can require additional capability, available support and compatible resources at other grains.