[Merged by Bors] - feat: Product of injective functions on sets #12656
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YaelDillies
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May 4, 2024
YaelDillies
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| variable {α₁ α₂ β₁ β₂ : Type*} {s₁ : Set α₁} {s₂ : Set α₂} {t₁ : Set β₁} {t₂ : Set β₂} | ||
| {f₁ : α₁ → β₁} {f₂ : α₂ → β₂} {g₁ : β₁ → α₁} {g₂ : β₂ → α₂} | ||
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| lemma InjOn.prodMap (h₁ : s₁.InjOn f₁) (h₂ : s₂.InjOn f₂) : |
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I find dot notation for InjOn doesn't really read well, but won't block on it
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Why not use Prod.map in the statements?
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because it gets simplified to its definition as Prod_map (not a typo!!) is a simp lemma
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
urkud
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May 4, 2024
| @@ -1041,6 +1041,14 @@ theorem BijOn.image_eq (h : BijOn f s t) : f '' s = t := | |||
| h.surjOn.image_eq_of_mapsTo h.mapsTo | |||
| #align set.bij_on.image_eq Set.BijOn.image_eq | |||
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| lemma BijOn.forall {p : β → Prop} (hf : BijOn f s t) : (∀ b ∈ t, p b) ↔ ∀ a ∈ s, p (f a) where | |||
| mp h a ha := h _ $ hf.mapsTo ha | |||
| mpr h b hb := by obtain ⟨a, ha, rfl⟩ := hf.surjOn hb; exact h _ ha | |||
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Alternative proof: by rw [← hf.image_eq, forall_mem_image]
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Thanks! 🎉 |
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