Deliberately left as an exercise for the reader. It really is trivial, but it seems so obvious once it’s known that I’m honestly curious how obvious it is (or isn’t?) when it’s not already known.
Took me several minutes, and I’m still not 100% sure my proof is correct.
Edit: The one I was thinking of was more complicated than needed. Nal vagrtre a terngre guna sbhe raqf jvgu gjb jura jevggra va onfr a zvahf gjb.
Took me several minutes, and I’m still not 100% sure my proof is correct.
Edit: The one I was thinking of was more complicated than needed. Nal vagrtre a terngre guna sbhe raqf jvgu gjb jura jevggra va onfr a zvahf gjb.
That was the proof that I thought of as well.
Yep, that’s what I had.
More generally: Sbe nal vagrtre a terngre guna gjb gvzrf k, cvpx gur onfr (a zvahf k) gb jevgr a fhpu gung vg raqf va gur qvtvg k.