[Merged by Bors] - feat(data/nat/pairing): add some nat.pair lemmas
#8740
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JasonKYi
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Aug 18, 2021
JasonKYi
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eric-wieser
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eric-wieser
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eric-wieser
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eric-wieser
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eric-wieser
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| lemma supr_unpair {α} [complete_lattice α] (f : ℕ → ℕ → α) : | ||
| (⨆ n : ℕ, f n.unpair.1 n.unpair.2) = ⨆ i j : ℕ, f i j := | ||
| by rw [← (supr_prod : (⨆ i : ℕ × ℕ, f i.1 i.2) = _), ← nat.surjective_unpair.supr_comp] | ||
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| lemma infi_unpair {α} [complete_lattice α] (f : ℕ → ℕ → α) : | ||
| (⨅ n : ℕ, f n.unpair.1 n.unpair.2) = ⨅ i j : ℕ, f i j := | ||
| supr_unpair (show ℕ → ℕ → order_dual α, from f) |
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In your original application did you want the Union version? If so, you should probably add that one below these (proved in terms of them).
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Can I not directly apply the supr version in my use case?
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Not with a rw. It will work with an apply
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nat.pair lemmasnat.pair lemmas
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