Graph theory - minor improvements of Huneke's proof (#2415)
Graph theory - minor improvements of Huneke's proof (#2415)

* Graph theory: sum of vertex degrees is twice the number of edges

Changes in parts before GRAPH THEORY
* ~bj-eleq1w (renamaed ~eleq1w) moved from BJ's mathbox to main: @benjub please check if this is the right place, and if the comment should be adjusted esp. if the tag "(Proof modification is discouraged.)" should be removed.
* ~rabeqi, ~rabeqif, ~ bn21 (renamed ~ssrab3), ~funfnd, ~ elrabd moved from mathboxes to main
* ~elneldisj and ~elnelun generalized
* comment for df-pr enhanced ("proper unordered pairs" explained)
* theorems ~prproe and ~3elpr2eq about proper unordered pairs added
* ~rabasiun removed (duplicate)
* ~hashres, ~hashreshashfun added
*  ~fsummsnunz, ~fsumsplitsnun generalized
* spelling of "power set" (vs. "powerset") harmonized

Changes in part GRAPH THEORY
* ~iedgedg, ~upgrop added
* ~edglnl, ~numedglnl, ~vtxdgop  added
* ~upgrres, ~umgrres, ~usgrres added
* ~vtxdginducedm1, ~vtxdginducedm1fi added
* ~finsumvtxdg2sstep and ~finsumvtxdg2size (main result of this PR, dedicated to Norm, because I think this is an example for his (and my!) motivation for working with Metamath.

* Review remarks incorporated

* Review remarks of @benjub incorporated
* Corrections of typos detected by GL

* Graph theory, Goldbach conjecture, misc.

set.mm main (misc.):
* 3imp231 moved from AS's mathbox
* correction in dv-statement for ~sumvtxdg2size
* convention for order of suffixes enhanced

set.mm main (graph theory):
* ~usgr1th , ~finsumvtxdgeven, ~vtxdgoddnumeven added

set.mm AV's mathbox:
* alternate definition e// for negated membership e/ and related theorems added
* therorems ~evenltle, ~odd2prm2, ~even3prm2 and ~mogoldbblem for even and oidd numbers added
* GoldbachOdd renamed to GoldbachOddW and GoldbachOddALTV renamed to GoldbachOdd  (as suggested by GL)
* Header comment of section "Goldbach's conjectures" revised (including a glossary)
* comments and label fragments for theorems about Goldbach's conjecture adjusted
* theorems ~sbgoldbb, ~sgoldbeven3prm, ~sbgoldbm, ~mogoldbb, ~sbgoldbmb, ~sbgoldbo about Goldbach's conjecture added
* bibliographic references added/revised (as suggested by BJ)

mmset.raw.html
* bibliographic references enhanced (as suggested by BJ)

* Bibliographic reference corrected

* Bibliographic reference corrected (2)

* Revision after review

set.mm main (graph theory):
* ~fusgrfupgrfs, ~fusgrvtxdgonume added
* ~usgr1th renamed ~fusgr1th, comment corrected, proof shortened
* correction "much" -> "many" and "e.g. " -> "e.g., "

mmset.raw.html
* bibliographic references adjusted (html instead of pdf)

* Proofs minimized using 3imp231

Proofs minimized using 3imp231: ~3imp3i2an, ~sotri2, ~oawordri, ~undifixp, ~eel12131

* Revision after 2. review

* comment for df-nelbr enhanced
* theorem ~dfnelbr2 added
* Goldbach partion -> Goldbach partition

* Graph theory - minor improvements of Huneke's proof

* ~ elinsn added
* comment of ~df-fusgr adjusted
* ~frcond3 split into 2 theorems
* lemmata for ~frgrncvvdeq renamed and optimized
* comments of ~frgrwopreg and its lemmata adjusted
metamath/set.mm,metamath/set.mm,metamath/set.mm