[Merged by Bors] - feat(data/setoid/partition): indexed partition #7910

PatrickMassot · 2021-06-12T21:28:17Z

from LTE
Note that data/setoid/partition.lean, which already existed before this
PR, is currently not imported anywhere in mathlib. But it is used in LTE
and will be used in the next PR, in relation to locally constant
functions.

from LTE Note that data/setoid/partition.lean, which already existed before this PR, is currently not imported anywhere in mathlib. But it is used in LTE and will be used in the next PR, in relation to locally constant functions.

src/data/quot.lean

src/data/setoid/basic.lean

src/data/setoid/partition.lean

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

eric-wieser · 2021-06-13T11:55:54Z

src/data/setoid/partition.lean

+/-- The equivalence relation associated to an indexed partition. Two
+elements are equivalent if they belong to the same set of the partition. -/
+protected def setoid (hs : indexed_partition s) : setoid α :=
+{ r := λ x y, ∃ i, x ∈ s i ∧ y ∈ s i,


I think this whole definition golfs to setoid.ker hs.index?

This won't be definitionaly equal, so all proofs will break. I don't have time to play this game.

I think it's better here to use setoid.ker in this file - we have it for a reason, and it feels unnecessary to duplicate work when there's a nicer definition which also simplifies later proofs as Eric shows below.

You are the ones who talk about duplicating work. That file works, it is usable since it has been used without any problem. Now you want to duplicate work by redoing it differently. You are welcome do it, but I won't.

I think it's important to distinguish duplicating effort from duplicating code. Bhavik means that the API surface of mathlib has duplication (aka, the output of the work is duplicated), while Patrick is objecting to redoing the work.

You are welcome do it, but I won't.

I've pushed a change to that effect, which removes 20 lines of proofs.

src/data/quot.lean

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

eric-wieser

I'm slightly worried this mostly duplicates what we already have for setoid.ker. How much work is it to change LTE to use setoid.ker? Could you link to where it's used? Perhaps I'm overestimating the similarity

For other maintainers: how much weight does the argument "well LTE already uses it this way so we shouldn't change it now" hold?

src/data/setoid/partition.lean

eric-wieser · 2021-06-13T18:11:46Z

I should point out my comments above are not saying that this PR necessarily needs the change I'm suggesting, but drawing attention to it for other reviewers who I'll let make the final call

src/data/setoid/partition.lean

jcommelin · 2021-06-14T09:46:25Z

@eric-wieser The main use of indexed_partition is in src/prop_92/extension_profinite.lean.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>

…s `symm`

src/data/setoid/partition.lean

src/data/quot.lean

b-mehta · 2021-06-18T13:12:28Z

src/data/setoid/basic.lean

@@ -36,8 +36,12 @@ variables {α : Type*} {β : Type*}
 /-- A version of `setoid.r` that takes the equivalence relation as an explicit argument. -/
 def setoid.rel (r : setoid α) : α → α → Prop := @setoid.r _ r

+/-- A version of `quotient.eq` compatible with `setoid.rel`, to make rewriting possible. -/
+lemma quotient.eq_rel {r : setoid α} {x y} : ⟦x⟧ = ⟦y⟧ ↔ r.rel x y := quotient.eq


This version looks odd to me: the quotient square brackets are usually when the setoid argument is a typeclass, but here it's implicit...

You're quite right, my mistake:

Suggested change

lemma quotient.eq_rel {r : setoid α} {x y} : ⟦x⟧ = ⟦y⟧ ↔ r.rel x y := quotient.eq

lemma quotient.eq_rel [setoid α] {x y} : ⟦x⟧ = ⟦y⟧ ↔ r.rel x y := quotient.eq

This change breaks things downstream

I just removed the lemma stated this way, it's weird to use rel for the typeclass version anyway.

This is a horrible can of worms: Zulip

src/data/setoid/partition.lean

b-mehta · 2021-06-18T13:19:08Z

src/data/setoid/partition.lean

+variables {ι α : Type*} {s : ι → set α} (hs : indexed_partition s)
+include hs
+
+lemma exists_mem (x : α) : ∃ i, x ∈ s i := ⟨hs.index x, hs.mem_index x⟩


It could be nice to have the exists_unique version of this using disjoint

src/data/setoid/basic.lean

jcommelin

Thanks 🎉

bors merge

from LTE Note that data/setoid/partition.lean, which already existed before this PR, is currently not imported anywhere in mathlib. But it is used in LTE and will be used in the next PR, in relation to locally constant functions. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

bors · 2021-06-29T17:54:51Z

Pull request successfully merged into master.

Build succeeded:

from LTE Note that data/setoid/partition.lean, which already existed before this PR, is currently not imported anywhere in mathlib. But it is used in LTE and will be used in the next PR, in relation to locally constant functions. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

feat(data/setoid/partition): indexed partition

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from LTE Note that data/setoid/partition.lean, which already existed before this PR, is currently not imported anywhere in mathlib. But it is used in LTE and will be used in the next PR, in relation to locally constant functions.

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Use some suggestion by Eric

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Update src/data/setoid/partition.lean

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Merge remote-tracking branch 'origin/master' into partition

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Make out computable to justify its existance

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[Merged by Bors] - feat(data/setoid/partition): indexed partition #7910

[Merged by Bors] - feat(data/setoid/partition): indexed partition #7910

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bors bot commented Jun 29, 2021

	lemma quotient.eq_rel {r : setoid α} {x y} : ⟦x⟧ = ⟦y⟧ ↔ r.rel x y := quotient.eq
	lemma quotient.eq_rel [setoid α] {x y} : ⟦x⟧ = ⟦y⟧ ↔ r.rel x y := quotient.eq

[Merged by Bors] - feat(data/setoid/partition): indexed partition #7910

[Merged by Bors] - feat(data/setoid/partition): indexed partition #7910

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