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rwbartonjohoelzl
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fix(data/set/basic): mark subset.refl as @[refl]
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analysis/measure_theory/outer_measure.lean

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@@ -193,7 +193,7 @@ let μ := λs, ⨅{f : ℕ → set α} (h : s ⊆ ⋃i, f i), ∑i, m (f i) in
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let f' := λi, f (nat.unpair i).1 (nat.unpair i).2 in
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have hf' : (⋃ (i : ℕ), s i) ⊆ (⋃i, f' i),
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from Union_subset $ assume i, subset.trans (hf i).left $ Union_subset_Union2 $ assume j,
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⟨nat.mkpair i j, begin simp [f'], simp [nat.unpair_mkpair], exact subset.refl _ end⟩,
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⟨nat.mkpair i j, begin simp [f'], simp [nat.unpair_mkpair] end⟩,
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have (∑i, of_real (ε' i)) = of_real ε, from aux hε,
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have (∑i, m (f' i)) ≤ (∑i, μ (s i)) + of_real ε,
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from calc (∑i, m (f' i)) = (∑p:ℕ×ℕ, m (f' (nat.mkpair p.1 p.2))) :

data/set/basic.lean

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@@ -61,7 +61,7 @@ subtype.exists
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-- TODO(Jeremy): write a tactic to unfold specific instances of generic notation?
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theorem subset_def {s t : set α} : (s ⊆ t) = ∀ x, x ∈ s → x ∈ t := rfl
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theorem subset.refl (a : set α) : a ⊆ a := assume x, id
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@[refl] theorem subset.refl (a : set α) : a ⊆ a := assume x, id
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@[trans] theorem subset.trans {a b c : set α} (ab : a ⊆ b) (bc : b ⊆ c) : a ⊆ c :=
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assume x h, bc (ab h)

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