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riccardobrasca committed Nov 27, 2023
1 parent 05a87c2 commit 3a8e53d
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25 changes: 5 additions & 20 deletions FltRegular/NumberTheory/AuxLemmas.lean
Original file line number Diff line number Diff line change
Expand Up @@ -164,10 +164,6 @@ lemma Ideal.inertiaDeg_comap_eq (e : S₁ ≃ₐ[R] S₂) (p : Ideal R) (P : Ide

end RamificationInertia

-- Mathlib/RingTheory/Nilpotent.lean
theorem not_isNilpotent_one {R : Type*} [MonoidWithZero R] [Nontrivial R] :
¬ IsNilpotent (1 : R) := fun ⟨_, H⟩ ↦ zero_ne_one (H.symm.trans (one_pow _))

open Polynomial IntermediateField

-- Mathlib/FieldTheory/Adjoin.lean
Expand Down Expand Up @@ -317,18 +313,6 @@ lemma Module.End.HasEigenvector.pow_apply {R} [CommRing R] {M} [AddCommGroup M]
(hv : f.HasEigenvector μ v) (n : ℕ) : (f ^ n) v = μ ^ n • v := by
induction n <;> simp [*, pow_succ f, hv.apply_eq_smul, smul_smul, pow_succ' μ]

-- Mathlib/Algebra/Module/Submodule/Basic.lean
lemma Submodule.restrictScalars_mul {A B C} [CommSemiring A] [CommSemiring B] [Semiring C]
[Algebra A B] [Algebra A C] [Algebra B C] [IsScalarTower A B C] {I J : Submodule B C} :
(I * J).restrictScalars A = I.restrictScalars A * J.restrictScalars A := by
apply le_antisymm
· intro x (hx : x ∈ I * J)
refine Submodule.mul_induction_on hx ?_ ?_
· exact fun m hm n hn ↦ Submodule.mul_mem_mul hm hn
· exact fun _ _ ↦ add_mem
· apply Submodule.mul_le.mpr
exact fun m hm n hn ↦ Submodule.mul_mem_mul hm hn

-- Mathlib/Logic/Equiv/Defs.lean
lemma EquivLike.coe_coe {E α β : Sort*} [EquivLike E α β] (e : E) :
((e : α ≃ β) : α → β) = e := rfl
Expand Down Expand Up @@ -1070,8 +1054,8 @@ lemma Matrix.eval_det_add_X_smul {n} [Fintype n] [DecidableEq n] {R} [CommRing R
(A) (M : Matrix n n R) :
(det (A + (X : R[X]) • M.map C)).eval 0 = (det A).eval 0 := by
simp only [eval_det, map_zero, map_add, eval_add, Algebra.smul_def, _root_.map_mul]
simp only [algebraMap_eq_smul, matPolyEquiv_smul_one, map_X, X_mul, eval_mul_X, mul_zero,
add_zero]
simp only [Algebra.algebraMap_eq_smul_one, matPolyEquiv_smul_one, map_X, X_mul, eval_mul_X,
mul_zero, add_zero]

-- Mathlib/LinearAlgebra/Matrix/Trace.lean
lemma Matrix.trace_submatrix_succ {n : ℕ} {R} [CommRing R] (M : Matrix (Fin n.succ) (Fin n.succ) R) :
Expand Down Expand Up @@ -1136,14 +1120,15 @@ lemma Matrix.det_one_add_smul {n} [Fintype n] [DecidableEq n] {R} [CommRing R] (
(M : Matrix n n R) : det (1 + r • M) =
1 + trace M * r + (det (1 + (X : R[X]) • M.map C)).divX.divX.eval r * r ^ 2 := by
have := congr_arg (eval r) (Matrix.det_one_add_X_smul M)
simp only [eval_det, coe_scalar, map_add, _root_.map_one, eval_add, eval_one, eval_smul, eval_X,
simp only [eval_det, scalar_apply, map_add, _root_.map_one, eval_add, eval_one, eval_smul, eval_X,
smul_eq_mul, eval_mul, eval_pow] at this
convert this
rw [Algebra.smul_def X, _root_.map_mul]
have : matPolyEquiv (M.map C) = C M
· ext; simp only [matPolyEquiv_coeff_apply, map_apply, coeff_C]; rw [ite_apply, ite_apply]; rfl
simp only [algebraMap_eq_smul, matPolyEquiv_smul_one, map_X, X_mul, eval_mul_X, this,
simp only [Algebra.algebraMap_eq_smul_one, matPolyEquiv_smul_one, map_X, X_mul, eval_mul_X, this,
Algebra.mul_smul_comm, mul_one, eval_C]
exact Matrix.smul_eq_mul_diagonal _ _

lemma Algebra.norm_one_add_smul {A B} [CommRing A] [CommRing B] [Algebra A B]
[Module.Free A B] [Module.Finite A B] (a : A) (x : B) :
Expand Down
3 changes: 1 addition & 2 deletions FltRegular/NumberTheory/Hilbert90.lean
Original file line number Diff line number Diff line change
Expand Up @@ -26,8 +26,7 @@ def φ := (finEquivZpowers _ (isOfFinOrder_of_finite σ)).symm
variable {σ}

lemma : ∀ (n : ℕ), φ σ ⟨σ ^ n, hσ _⟩ = n % (orderOf σ) := fun n ↦ by
simpa [Fin.ext_iff] using
@finEquivZpowers_symm_apply _ _ _ (isOfFinOrder_of_finite σ) n ⟨n, by simp⟩
simpa [Fin.ext_iff] using finEquivZpowers_symm_apply _ (isOfFinOrder_of_finite σ) n

noncomputable
def cocycle : (L ≃ₐ[K] L) → Lˣ := fun τ ↦ ∏ i in range (φ σ ⟨τ, hσ τ⟩), Units.map (σ ^ i) (ηu hη)
Expand Down
2 changes: 1 addition & 1 deletion lake-manifest.json
Original file line number Diff line number Diff line change
Expand Up @@ -49,7 +49,7 @@
{"url": "https://github.com/leanprover-community/mathlib4.git",
"type": "git",
"subDir": null,
"rev": "83d4f222771f491b351d70b070406481f5d2b2ba",
"rev": "313ebb4380e5fca7f4cf6a610956a4b5a934235a",
"name": "mathlib",
"manifestFile": "lake-manifest.json",
"inputRev": null,
Expand Down

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