Open mechvel opened 2 months ago
We already have many different formalisations of this notion:
https://github.com/agda/agda-stdlib/blob/master/src/Data/List/Relation/Binary/BagAndSetEquality.agda
while I would welcome a proof that bidirectional subset inclusion implies these, I really don't think we want to be adding yet another relation.
If we do add this new relation, I think we should name it the same as Relation.Unary._≐_
, which is defined in an analogous way on predicates
See also the recently added (#2070 / #2071 ) https://github.com/agda/agda-stdlib/blob/master/src/Relation/Binary/Construct/Interior/Symmetric.agda It seems that what you are asking for is the instance of this construction for the $\subseteq$ preorder...
It seems that what you are asking for is the instance of this construction for the preorder...
I agreed, but I still really don't think we should add it as a first class relation, merely a proof that the construction is equivalent to the current definitions of set equality.
I suggest to add to standard library the following items.
To Data.List.Relation.Binary.Subset.Setoid:
To Data.List.Relation.Binary.Subset.Setoid.Properties:
This is because the above items are usable.