feat(set_theory/cardinal): more lemmas on cardinality #595
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johoelzl
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Jan 15, 2019
data/set/basic.lean
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| @@ -823,6 +823,10 @@ theorem image_inter {f : α → β} {s t : set α} (H : injective f) : | |||
| f '' s ∩ f '' t = f '' (s ∩ t) := | |||
| image_inter_on (assume x _ y _ h, H h) | |||
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| theorem surjective_onto_image {f : α → β} {s : set α} : | |||
| surjective (λ p, ⟨f p.1, ⟨p.1, p.2, rfl⟩⟩ : s → f '' s) := | |||
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It would be nicer to use the lemma mem_image_of_mem (like mem_range_self) in the later proof.
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I think this function should be given a name, so that the proofs don't appear in the statement of the theorem.
set_theory/cardinal.lean
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| exact subtype.mk.inj (eq_of_heq H2) | ||
| end⟩⟩ | ||
| ≤ mk (Σ i, f i) : mk_le_of_surjective $ show surjective | ||
| (show (Σ i, f i) → (⋃ i, f i), from λ ⟨i, x, hx⟩, ⟨x, mem_Union.2 ⟨i, hx⟩⟩), from |
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I think the proof would be nicer as (NOTE: I didn't test this proof)
let f : (Σ i, f i) → (⋃ i, f i) := λ ⟨i, x, hx⟩, ⟨x, mem_Union.2 ⟨i, hx⟩⟩ in
have surjective f := λ ⟨x, hx⟩, let ⟨i, hi⟩ := mem_Union.1 hx in ⟨⟨i, x, hi⟩, rfl⟩,
mk_le_of_surjective this
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Thanks for the feedback. Is |
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cipher1024
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Feb 8, 2019
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