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lines changed Original file line number Diff line number Diff line change @@ -1059,15 +1059,15 @@ inv_lt_iff_inv_lt.trans $ by rw [inv_one]
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/-- The inverse map `λ x, x⁻¹` is an order isomorphism between `ℝ≥0∞` and its `order_dual` -/
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@[simps apply]
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- def inv_order_iso : ℝ≥0 ∞ ≃o order_dual ℝ≥0 ∞ :=
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+ def _root_.order_iso.inv_ennreal : ℝ≥0 ∞ ≃o order_dual ℝ≥0 ∞ :=
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{ to_fun := λ x, x⁻¹,
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inv_fun := λ x, x⁻¹,
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left_inv := @ennreal.inv_inv,
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right_inv := @ennreal.inv_inv,
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map_rel_iff' := λ a b, ennreal.inv_le_inv }
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@[simp]
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- lemma inv_order_iso_symm_apply : inv_order_iso .symm a = a⁻¹ := rfl
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+ lemma _root_.order_iso.inv_ennreal_symm_apply : order_iso.inv_ennreal .symm a = a⁻¹ := rfl
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lemma pow_le_pow_of_le_one {n m : ℕ} (ha : a ≤ 1 ) (h : n ≤ m) : a ^ m ≤ a ^ n :=
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begin
Original file line number Diff line number Diff line change @@ -425,11 +425,11 @@ infi_mul_right' h (λ _, ‹nonempty ι›)
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lemma inv_map_infi {ι : Sort *} {x : ι → ℝ≥0 ∞} :
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(infi x)⁻¹ = (⨆ i, (x i)⁻¹) :=
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- inv_order_iso .map_infi x
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+ order_iso.inv_ennreal .map_infi x
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lemma inv_map_supr {ι : Sort *} {x : ι → ℝ≥0 ∞} :
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(supr x)⁻¹ = (⨅ i, (x i)⁻¹) :=
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- inv_order_iso .map_supr x
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+ order_iso.inv_ennreal .map_supr x
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lemma inv_limsup {ι : Sort *} {x : ι → ℝ≥0 ∞} {l : filter ι} :
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(l.limsup x)⁻¹ = l.liminf (λ i, (x i)⁻¹) :=
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