Open MatthiasHu opened 4 months ago
@mzeuner What do you think?
Sorry for the late reply. I guess there is a general question about whether we want a (bounded) distributive lattice to be a poset with induced joins and meets or an algebraic structure with an induced order. I went for the latter when setting everything up, but I'm not sure anymore that that was the right choice. So I'm all for trying the other approach.
Here is an idea for an improvement in ZariskiLattice.Base .
The current set-quotient construction begins by defining a preorder (without using this name) and deriving the equivalence relation
_∼_
from that: https://github.com/agda/cubical/blob/6ce70a4934db4dac521c60399183b3b6e1bcf225/Cubical/Algebra/ZariskiLattice/Base.agda#L72-L83So the set-quotient is actually an instance of a general (not formalized yet, I think) preorder-to-poset construction. I propose to actually implement it as such and then to use the resulting poset structure to define the lattice structure more easily.
Advantages:
_∨z_
and_∧z_
operations._∨z_
and_∧z_
by hand, only the distributive law remains.Prerequisites:
Order.Preorder.Properties
)