What're the tagging rules for "transitive" separate sidewalks?

https://www.openstreetmap.org/way/619241252#map=19/53.805620/-1.532968&layers=N

1) The road has `cycleway:left = separate` (err this one doesn't, but the other side does -- pretend this is true)
2) The cycleway has `sidewalk:left = separate`

So by transitivity, the road has a separate sidewalk on the left side.

Should the road have `sidewalk:left = separate` or `sidewalk:left = no`? Is it "double tagging" to mark this on both the road and cycleway? It's more like repeating a pointer to something else, rather than mapping it twice.