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fix SMul
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AntoineChambert-Loir committed Jul 3, 2024
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16 changes: 0 additions & 16 deletions Mathlib/Data/Set/Pointwise/SMul.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1040,22 +1040,6 @@ lemma inv_op_smul_set_distrib (a : α) (s : Set α) : (op a • s)⁻¹ = a⁻¹
lemma smul_set_disjoint_iff : Disjoint (a • s) (a • t) ↔ Disjoint s t := by
simp [disjoint_iff, ← smul_set_inter]

example (a : α) (s : Set β) : a • s = (fun b ↦ a • b) '' s := by
rw [@image_smul]

@[to_additive]
lemma smul_set_iInter {ι : Type*} (a : α) (s : ι → Set β) :
(a • ⋂ i, s i) = ⋂ i, a • s i := by
obtain _ | _ := isEmpty_or_nonempty ι
· refine' Eq.trans _ (Set.iInter_of_empty _).symm
rw [Set.iInter_of_empty]
exact Set.smul_set_univ
· rw [← image_smul, Set.InjOn.image_iInter_eq ?_]
simp only [image_smul]
apply Function.Injective.injOn
intro x y
simp only [smul_left_cancel_iff, imp_self]

end Group

section GroupWithZero
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