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5 changes: 4 additions & 1 deletion Mathbin/Algebra/Lie/CartanMatrix.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
! This file was ported from Lean 3 source module algebra.lie.cartan_matrix
! leanprover-community/mathlib commit 65ec59902eb17e4ab7da8d7e3d0bd9774d1b8b99
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -15,6 +15,9 @@ import Mathbin.Data.Matrix.Notation
/-!
# Lie algebras from Cartan matrices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Split semi-simple Lie algebras are uniquely determined by their Cartan matrix. Indeed, if `A` is
an `l × l` Cartan matrix, the corresponding Lie algebra may be obtained as the Lie algebra on
`3l` generators: $H_1, H_2, \ldots H_l, E_1, E_2, \ldots, E_l, F_1, F_2, \ldots, F_l$
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5 changes: 4 additions & 1 deletion Mathbin/Algebra/Module/Zlattice.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
! This file was ported from Lean 3 source module algebra.module.zlattice
! leanprover-community/mathlib commit a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Group.FundamentalDomain
/-!
# ℤ-lattices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Let `E` be a finite dimensional vector space over a `normed_linear_ordered_field` `K` with a solid
norm and that is also a `floor_ring`, e.g. `ℚ` or `ℝ`. A (full) ℤ-lattice `L` of `E` is a discrete
subgroup of `E` such that `L` spans `E` over `K`.
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5 changes: 4 additions & 1 deletion Mathbin/Analysis/Complex/Polynomial.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
! This file was ported from Lean 3 source module analysis.complex.polynomial
! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.FieldTheory.IsAlgClosed.Basic
/-!
# The fundamental theorem of algebra
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file proves that every nonconstant complex polynomial has a root using Liouville's theorem.
As a consequence, the complex numbers are algebraically closed.
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4 changes: 2 additions & 2 deletions Mathbin/Analysis/MeanInequalitiesPow.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -318,7 +318,7 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
· simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
· have A : p - 10 := ne_of_gt (sub_pos.2 h'p)
simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
div_eq_inv_mul, rpow_one, mul_one]
ENNReal.div_eq_inv_mul, rpow_one, mul_one]
ring
#align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow

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5 changes: 4 additions & 1 deletion Mathbin/CategoryTheory/Monoidal/Limits.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module category_theory.monoidal.limits
! leanprover-community/mathlib commit 744d59af0b28d0c42f631038627df9b85ae1d1ce
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Limits.HasLimits
/-!
# `lim : (J ⥤ C) ⥤ C` is lax monoidal when `C` is a monoidal category.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
When `C` is a monoidal category, the functorial association `F ↦ limit F` is lax monoidal,
i.e. there are morphisms
* `lim_lax.ε : (𝟙_ C) → limit (𝟙_ (J ⥤ C))`
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5 changes: 4 additions & 1 deletion Mathbin/CategoryTheory/Preadditive/Schur.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
! This file was ported from Lean 3 source module category_theory.preadditive.schur
! leanprover-community/mathlib commit 58a272265b5e05f258161260dd2c5d247213cbd3
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -16,6 +16,9 @@ import Mathbin.FieldTheory.IsAlgClosed.Spectrum

/-!
# Schur's lemma
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
We first prove the part of Schur's Lemma that holds in any preadditive category with kernels,
that any nonzero morphism between simple objects
is an isomorphism.
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5 changes: 4 additions & 1 deletion Mathbin/CategoryTheory/Sites/CompatibleSheafification.lean
Expand Up @@ -4,14 +4,17 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
! This file was ported from Lean 3 source module category_theory.sites.compatible_sheafification
! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Sites.CompatiblePlus
import Mathbin.CategoryTheory.Sites.Sheafification

/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
In this file, we prove that sheafification is compatible with functors which
preserve the correct limits and colimits.
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5 changes: 4 additions & 1 deletion Mathbin/Data/Polynomial/UnitTrinomial.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
! This file was ported from Lean 3 source module data.polynomial.unit_trinomial
! leanprover-community/mathlib commit 302eab4f46abb63de520828de78c04cb0f9b5836
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.Data.Polynomial.Mirror
/-!
# Unit Trinomials
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file defines irreducible trinomials and proves an irreducibility criterion.
## Main definitions
Expand Down
20 changes: 18 additions & 2 deletions Mathbin/Data/Real/Ennreal.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
! This file was ported from Lean 3 source module data.real.ennreal
! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -303,6 +303,14 @@ theorem toReal_eq_zero_iff (x : ℝ≥0∞) : x.toReal = 0 ↔ x = 0 ∨ x = ∞
simp [ENNReal.toReal, to_nnreal_eq_zero_iff]
#align ennreal.to_real_eq_zero_iff ENNReal.toReal_eq_zero_iff

theorem toNNReal_ne_zero : a.toNNReal ≠ 0 ↔ a ≠ 0 ∧ a ≠ ∞ :=
a.toNNReal_eq_zero_iff.Not.trans not_or
#align ennreal.to_nnreal_ne_zero ENNReal.toNNReal_ne_zero

theorem toReal_ne_zero : a.toReal ≠ 0 ↔ a ≠ 0 ∧ a ≠ ∞ :=
a.toReal_eq_zero_iff.Not.trans not_or
#align ennreal.to_real_ne_zero ENNReal.toReal_ne_zero

#print ENNReal.toNNReal_eq_one_iff /-
theorem toNNReal_eq_one_iff (x : ℝ≥0∞) : x.toNNReal = 1 ↔ x = 1 :=
by
Expand All @@ -317,6 +325,14 @@ theorem toReal_eq_one_iff (x : ℝ≥0∞) : x.toReal = 1 ↔ x = 1 := by
rw [ENNReal.toReal, NNReal.coe_eq_one, ENNReal.toNNReal_eq_one_iff]
#align ennreal.to_real_eq_one_iff ENNReal.toReal_eq_one_iff

theorem toNNReal_ne_one : a.toNNReal ≠ 1 ↔ a ≠ 1 :=
a.toNNReal_eq_one_iff.Not
#align ennreal.to_nnreal_ne_one ENNReal.toNNReal_ne_one

theorem toReal_ne_one : a.toReal ≠ 1 ↔ a ≠ 1 :=
a.toReal_eq_one_iff.Not
#align ennreal.to_real_ne_one ENNReal.toReal_ne_one

@[simp]
theorem coe_ne_top : (r : ℝ≥0∞) ≠ ∞ :=
WithTop.coe_ne_top
Expand Down Expand Up @@ -1508,7 +1524,7 @@ instance : Inv ℝ≥0∞ :=
instance : DivInvMonoid ℝ≥0∞ :=
{ (inferInstance : Monoid ℝ≥0∞) with inv := Inv.inv }

theorem div_eq_inv_mul : a / b = b⁻¹ * a := by rw [div_eq_mul_inv, mul_comm]
protected theorem div_eq_inv_mul : a / b = b⁻¹ * a := by rw [div_eq_mul_inv, mul_comm]
#align ennreal.div_eq_inv_mul ENNReal.div_eq_inv_mul

@[simp]
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/FieldTheory/IsAlgClosed/Classification.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -17,6 +17,9 @@ import Mathbin.Data.Zmod.Algebra
/-!
# Classification of Algebraically closed fields
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file contains results related to classifying algebraically closed fields.
## Main statements
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/FieldTheory/IsAlgClosed/Spectrum.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
! This file was ported from Lean 3 source module field_theory.is_alg_closed.spectrum
! leanprover-community/mathlib commit 58a272265b5e05f258161260dd2c5d247213cbd3
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.FieldTheory.IsAlgClosed.Basic
/-!
# Spectrum mapping theorem
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file develops proves the spectral mapping theorem for polynomials over algebraically closed
fields. In particular, if `a` is an element of an `𝕜`-algebra `A` where `𝕜` is a field, and
`p : 𝕜[X]` is a polynomial, then the spectrum of `polynomial.aeval a p` contains the image of the
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/LinearAlgebra/Eigenspace/IsAlgClosed.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
! This file was ported from Lean 3 source module linear_algebra.eigenspace.is_alg_closed
! leanprover-community/mathlib commit 6b0169218d01f2837d79ea2784882009a0da1aa1
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.FieldTheory.IsAlgClosed.Spectrum
/-!
# Eigenvectors and eigenvalues over algebraically closed fields.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
* Every linear operator on a vector space over an algebraically closed field has an eigenvalue.
* The generalized eigenvectors span the entire vector space.
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/LinearAlgebra/Matrix/Charpoly/Eigs.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mohanad Ahmed
! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.eigs
! leanprover-community/mathlib commit 48dc6abe71248bd6f4bffc9703dc87bdd4e37d0b
! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.FieldTheory.IsAlgClosed.Basic
/-!
# Eigenvalues are characteristic polynomial roots.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
In fields we show that:
* `matrix.det_eq_prod_roots_charpoly_of_splits`: the determinant (in the field of the matrix)
Expand Down
3 changes: 2 additions & 1 deletion Mathbin/MeasureTheory/Function/L1Space.lean
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
! This file was ported from Lean 3 source module measure_theory.function.l1_space
! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -516,6 +516,7 @@ theorem integrable_const_iff {c : β} : Integrable (fun x : α => c) μ ↔ c =
rw [integrable, and_iff_right this, has_finite_integral_const_iff]
#align measure_theory.integrable_const_iff MeasureTheory.integrable_const_iff

@[simp]
theorem integrable_const [IsFiniteMeasure μ] (c : β) : Integrable (fun x : α => c) μ :=
integrable_const_iff.2 <| Or.inr <| measure_lt_top _ _
#align measure_theory.integrable_const MeasureTheory.integrable_const
Expand Down

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