Some universes in Sets
are necessarily equal
#144
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By inserting
Set Printing Universes. About Sets.
on line 86 ofInstance/Sets.v
one can check, that according to Coq the universeso, h, sh, p
in the definition ofSets
all need to be equal. I observed this with Coq v8.17 and the master branch.The patch removes the universe variables
h, sh, p
from the signature ofSets
and substitutes them witho
. This should makeSets
a bit easier to understand and use, when explicit universes are needed.The changes to
Adjunction
are there to deal with the new definition. One universe variable could be removed, because it only occurred as argument toSets
.I am not entirely sure how the equalities arise. By using
About
some more I found the following (forSets@{o h so sh p}
):Category
forcessh ≤ p
obj := SetoidObject
forceso, p < so
SetoidMorphism
forceso ≤ p
ando = h
.SetoidMorphism_Setoid@{o h p}
forceso = h = p
.Similar equations arise in other definitions, but I do not use these as much as
Sets
.