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[Merged by Bors] - chore(data/finset/pointwise): {a} • t = a • t #17072

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[Merged by Bors] - chore(data/finset/pointwise): {a} • t = a • t #17072

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chore(data/finset/pointwise): `{a} • t = a • t`
YaelDillies Oct 19, 2022
42f8402
unsimp singleton_smul_singleton
YaelDillies Oct 23, 2022
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6 changes: 3 additions & 3 deletions src/data/finset/pointwise.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -659,9 +659,7 @@ nonempty.of_image₂_left
nonempty.of_image₂_right
@[to_additive] lemma smul_singleton (b : β) : s • ({b} : finset β) = s.image (• b) :=
image₂_singleton_right
@[to_additive] lemma singleton_smul (a : α) : ({a} : finset α) • t = t.image ((•) a) :=
image₂_singleton_left
@[simp, to_additive] lemma singleton_smul_singleton (a : α) (b : β) :
@[to_additive] lemma singleton_smul_singleton (a : α) (b : β) :
({a} : finset α) • ({b} : finset β) = {a • b} :=
image₂_singleton

Expand Down Expand Up @@ -782,6 +780,8 @@ lemma coe_smul_finset (a : α) (s : finset β) : (↑(a • s) : set β) = a •
@[simp, to_additive] lemma smul_finset_nonempty : (a • s).nonempty ↔ s.nonempty :=
nonempty.image_iff _
@[to_additive] lemma nonempty.smul_finset (hs : s.nonempty) : (a • s).nonempty := hs.image _
@[simp, to_additive] lemma singleton_smul (a : α) : ({a} : finset α) • t = a • t :=
image₂_singleton_left

@[to_additive, mono]
lemma smul_finset_subset_smul_finset : s ⊆ t → a • s ⊆ a • t := image_subset_image
Expand Down