feat(topology/opens): open_embedding_of_le (#3597)
feat(topology/opens): open_embedding_of_le (#3597)

Add `lemma open_embedding_of_le {U V : opens α} (i : U ≤ V) : open_embedding (set.inclusion i)`.

Also, I was finding it quite inconvenient to have `x ∈ U` for `U : opens X` being unrelated to `x ∈ (U : set X)`. I propose we just add the simp lemmas in this PR that unfold to the set-level membership operation.

(I'd be happy to go the other way if someone has a strong opinion here; just that we pick a simp normal form for talking about membership and inclusion of opens.)



Co-authored-by: Scott Morrison <63f04b4d96235eb042cc46d94f14d241d2a26722@gmail.com>

leanprover-community/mathlib,leanprover-community/mathlib