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[Merged by Bors] - feat(model_theory/basic): Substructures #7762
[Merged by Bors] - feat(model_theory/basic): Substructures #7762
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It might be worth the effort to instead define
closure
as alower_adjoint (coe : L.substructure M → set M)
and get a lot of the following lemmas (and quite a few additional ones!) for free. However,lower_adjoint
doesn't seem to be used yet in mathlib, so it's fine if you want to leave that to someone else.There was a problem hiding this comment.
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Done!
There's probably a better way to connect
lower_adjoint
togi
, but it does require an additional assumption (that the upper adjoint has the property thatu x <= u y
impliesx <= y
). I think this could at least be done at the level ofset_like
, but perhaps that's for a different PR.