The phrase "a general proof for" is correct and usable in written English.
It can be used when discussing a broad or overarching demonstration of a concept or theorem in various fields, such as mathematics or logic.
Example: "The mathematician presented a general proof for the theorem, which could be applied to multiple cases."
Alternatives: "a universal demonstration of" or "a comprehensive validation for".
(I have verified, via Maxima, that this is true for 2 n-way RIL up to n = 98. A general proof continues to elude me).
Whereas I have verified this for several individual networks with vertices of indegree 3 or 4, I do not have a general proof.
Through design and process modification many of these constraints have been addressed, and a microfluidics-based device capable of real-time monitoring of the pH change caused by Lactobacillus casei fermentation is presented as a general proof-of-concept for a wide array of possible devices.
Before discussing the general proof for any tree graph with multiple initially infected individuals, we consider two very simple example networks which will serve to motivate and illustrate the method of proof.
A completely general proof net framework for the extended Lambek calculi, with a correctness criterion based on rewriting, has been developed in Moot and Puite 2002 and Moot 2007.
Kreutz, C., Kählig, H., Konrat, R. & Micura, R. A general approach for the identification of site-specific RNA binders by 19F NMR spectroscopy: proof of concept.
Aristotle reports (Posterior Analytics. i.5, cf. Metaphysics xiii.2) that whereas mathematicians proved theorems such as a : b = c : d => a : c = b : d (alternando) separately for number, lines, planes, and solids, now there is one single general or universal proof for all (see Section 3).
But their application is limited to certain sub-problems, and do not yield a fully general proof of the lack of constraints for arbitrary I. [4.] This argument, especially the second illustration of it, is similar to the one in Horwich 1987, p 124-128.
A more general proof in the same vein is presented in Olsson (2002).
We have worked through a simple illustration of the general result claimed above, but this case is sufficiently representative for the general proof to be reconstructed.
