[Merged by Bors] - chore(topology/separation): Extract set product lemma
#14958
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YaelDillies
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| @@ -617,7 +617,8 @@ begin | |||
| ∑ i in s.preimage sum.inr (sum.inr_injective.inj_on _), (λ x, g x • v x) (sum.inr i) = 0, | |||
| { rw [finset.sum_preimage', finset.sum_preimage', ← finset.sum_union, ← finset.filter_or], | |||
| { simpa only [← mem_union, range_inl_union_range_inr, mem_univ, finset.filter_true] }, | |||
| { exact finset.disjoint_filter.2 (λ x hx, disjoint_left.1 is_compl_range_inl_range_inr.1) } }, | |||
| { exact finset.disjoint_filter.2 | |||
| (λ x _ hx, disjoint_left.1 is_compl_range_inl_range_inr.1 hx) } }, | |||
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Why did this proof become longer?
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It's because I changed disjoint_left to have a semi-implicit argument on the RHS. It seems to be the right choice everywhere but here.
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Please mention this in the commit message. Otherwise LGTM.
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urkud
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Jun 27, 2022
| lemma _root_.disjoint.inter_eq : disjoint s t → s ∩ t = ∅ := disjoint.eq_bot | ||
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| lemma disjoint_left : disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → a ∉ t := forall_congr $ λ _, not_and | ||
| lemma disjoint_right : disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [disjoint.comm, disjoint_left] |
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Idea for the future: some lemmas in this file have disjoint in the name and s ∩ t = ∅ in the statement. It would be nice to fix this.
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This is what #14950 does 😄 (for some of them).
| @@ -617,7 +617,8 @@ begin | |||
| ∑ i in s.preimage sum.inr (sum.inr_injective.inj_on _), (λ x, g x • v x) (sum.inr i) = 0, | |||
| { rw [finset.sum_preimage', finset.sum_preimage', ← finset.sum_union, ← finset.filter_or], | |||
| { simpa only [← mem_union, range_inl_union_range_inr, mem_univ, finset.filter_true] }, | |||
| { exact finset.disjoint_filter.2 (λ x hx, disjoint_left.1 is_compl_range_inl_range_inr.1) } }, | |||
| { exact finset.disjoint_filter.2 | |||
| (λ x _ hx, disjoint_left.1 is_compl_range_inl_range_inr.1 hx) } }, | |||
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Please mention this in the commit message. Otherwise LGTM.
bors d+
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✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with |
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Thanks both! bors merge |
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Jun 28, 2022
Move `prod_subset_compl_diagonal_iff_disjoint` to `data.set.prod`, where it belongs. Delete `diagonal_eq_range_diagonal_map` because it duplicates `set.diagonal_eq_range`. Move `set.disjoint_left`/`set.disjoint_right` to `data.set.basic` to avoid an import cycle. Make variable semi-implicit in the RHS of `disjoint_left` and `disjoint_right`.
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Pull request successfully merged into master. Build succeeded: |
bors
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set product lemmaset product lemma
awainverse
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Jun 28, 2022
Move `prod_subset_compl_diagonal_iff_disjoint` to `data.set.prod`, where it belongs. Delete `diagonal_eq_range_diagonal_map` because it duplicates `set.diagonal_eq_range`. Move `set.disjoint_left`/`set.disjoint_right` to `data.set.basic` to avoid an import cycle. Make variable semi-implicit in the RHS of `disjoint_left` and `disjoint_right`.
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Move
prod_subset_compl_diagonal_iff_disjointtodata.set.prod, where it belongs. Deletediagonal_eq_range_diagonal_mapbecause it duplicatesset.diagonal_eq_range. Moveset.disjoint_left/set.disjoint_righttodata.set.basicto avoid an import cycle.Make variable semi-implicit in the RHS of
disjoint_leftanddisjoint_right.