[Merged by Bors] - feat(data/fintype/basic): card_sum, card_subtype_or #8490
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pechersky
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Aug 1, 2021
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pechersky
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- depends on: [Merged by Bors] - feat(logic/embedding): subtype_or_{embedding,equiv} #8489
Provide explicit embedding from a subtype of a disjuction into a sum type. If the disjunction is disjoint, upgrade to an equiv. Additionally, provide `subtype.imp_embedding`, lowering a subtype along an implication.
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This reverts commit 4d8c0b0.
this prevents needing to infer an additional instance in rewrites
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🎉 Great news! Looks like all the dependencies have been resolved: 💡 To add or remove a dependency please update this issue/PR description. Brought to you by Dependent Issues (:robot: ). Happy coding! |
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eric-wieser
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| @[simp] theorem fintype.card_sum [fintype α] [fintype β] : | ||
| fintype.card (α ⊕ β) = fintype.card α + fintype.card β := | ||
| begin | ||
| classical, | ||
| rw [←finset.card_univ, univ_sum_type, finset.card_union_eq], | ||
| { simp [finset.card_univ] }, | ||
| { intros x hx, | ||
| suffices : (∃ (a : α), sum.inl a = x) ∧ ∃ (b : β), sum.inr b = x, | ||
| { obtain ⟨⟨a, rfl⟩, ⟨b, hb⟩⟩ := this, | ||
| simpa using hb }, | ||
| simpa using hx } | ||
| end |
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Does the old proof not work here?
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No, it doesn't, because the lemmas about the card over sigma types are expressed using big operator notation, which is later than this file.
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