Groupprops:Proof

This article is about the groupprops wiki itself

Proofs in Groupprops are usually given in fact articles. When a proof needs to be referred to in a definition article or survey article, a link to the proof is given. The link may be given either directly or using The proofat template.

Prior to giving the proof in a fact article, a background is set by defining the terms in the manner relevant to proof.

Symbol-free proof versus proof with symbols

The proofs given are usually with symbols. However, in some cases, a symbol-free proof may be clearer and more insightful. In this case, the symbol-free proof is presented in a separate section.

Different proofs using different formulations

Often, different formulations of the terms being defined give rise to different formulations of the proof. In this case, each proof may be presented in a separate subsection, with the subsection heading being something like In terms of .... For instance, check out the proof that every characteristic subgroup is normal.

Reference to other proofs and results in the proofs

If the proof uses important nontrivial results and lemmas, there may be a separate section (or subsection) titled Results used. Otherwise, minor references to other proofs and results can be sorted through links to the proofs of those results from within the proof.

Links to definitions of terms

Links to definitions of all terms used in the proof must be given.

Partial/sketchy proofs

Sketchy proofs are typically not given. If the complete proof details are too long or tedious to be given, the hard parts are abstracted into separate results and links to their proofs are provided (those links can be provided even before proofs of the results have been fully written up).