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riccardobrasca committed Jul 31, 2024
1 parent 015f73f commit 0309e08
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Showing 5 changed files with 13 additions and 13 deletions.
4 changes: 2 additions & 2 deletions FltRegular/NumberTheory/Cyclotomic/CyclRat.lean
Original file line number Diff line number Diff line change
Expand Up @@ -365,7 +365,7 @@ theorem dvd_last_coeff_cycl_integer [hp : Fact (p : ℕ).Prime] {ζ : 𝓞 L}
replace hy := congr_arg (b.basis.coord ((Fin.castOrderIso hdim.symm) ⟨i, hi⟩)) hy
rw [← b.basis.equivFun_symm_apply, ← b.basis.equivFun_symm_apply, LinearMap.map_sub,
b.basis.coord_equivFun_symm, b.basis.coord_equivFun_symm, ← smul_eq_mul,
← zsmul_eq_smul_cast] at hy
Int.cast_smul_eq_nsmul] at hy
obtain ⟨n, hn⟩ := b.basis.dvd_coord_smul ((Fin.castOrderIso hdim.symm) ⟨i, hi⟩) y m
rw [hn] at hy
simp only [Fin.castOrderIso_apply, Fin.cast_mk, Fin.castSucc_mk, Fin.eta, Hi, zero_sub,
Expand Down Expand Up @@ -418,7 +418,7 @@ theorem dvd_coeff_cycl_integer (hp : (p : ℕ).Prime) {ζ : 𝓞 L} (hζ : IsPri
simp only [Fin.castOrderIso_apply, Fin.cast_mk, Fin.castSucc_mk, Fin.eta, Basis.coord_apply,
sub_eq_iff_eq_add] at hy
obtain ⟨n, hn⟩ := b.basis.dvd_coord_smul ((Fin.cast hdim.symm) ⟨j, hj⟩) y m
rw [hy, ← smul_eq_mul, ← zsmul_eq_smul_cast, ← b.basis.coord_apply, ← Fin.cast_mk, hn]
rw [hy, ← smul_eq_mul, Int.cast_smul_eq_nsmul, ← b.basis.coord_apply, ← Fin.cast_mk, hn]
exact dvd_add (dvd_mul_right _ _) last_dvd

end IntFacts
8 changes: 4 additions & 4 deletions FltRegular/NumberTheory/Hilbert90.lean
Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@ lemma hφ : ∀ (n : ℕ), φ σ ⟨σ ^ n, hσ _⟩ = n % (orderOf σ) := fun 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)

lemma aux {a: ℕ} (h : a % orderOf σ = 0) :
lemma aux1 {a: ℕ} (h : a % orderOf σ = 0) :
∏ i in range a, (σ ^ i) (ηu hη) = 1 := by
obtain ⟨n, hn⟩ := (Nat.dvd_iff_mod_eq_zero _ _).2 h
rw [hn]
Expand All @@ -53,14 +53,14 @@ lemma aux {a: ℕ} (h : a % orderOf σ = 0) :
simp only [SetLike.coe_sort_coe, Subtype.coe_eta, Equiv.symm_apply_apply]
rfl

lemma aux1 {a b : ℕ} (h : a % orderOf σ = b % orderOf σ) :
lemma aux2 {a b : ℕ} (h : a % orderOf σ = b % orderOf σ) :
∏ i in range a, (σ ^ i) (ηu hη) = ∏ i in range b, (σ ^ i) (ηu hη) := by
wlog hab : b ≤ a generalizing a b
· exact (this h.symm (not_le.1 hab).le).symm
obtain ⟨c, hc⟩ := (Nat.dvd_iff_mod_eq_zero _ _).2 (Nat.sub_mod_eq_zero_of_mod_eq h)
rw [Nat.sub_eq_iff_eq_add hab] at hc
rw [hc, prod_range_add]
rw [aux hσ hη (Nat.mul_mod_right (orderOf σ) c), one_mul]
rw [aux1 hσ hη (Nat.mul_mod_right (orderOf σ) c), one_mul]
simp [pow_add, pow_mul, pow_orderOf_eq_one]

lemma cocycle_spec (hone : orderOf σ ≠ 1) : (cocycle hσ hη) σ = (ηu hη) := by
Expand Down Expand Up @@ -104,7 +104,7 @@ lemma is_cocycle_aux : ∀ (α β : (L ≃ₐ[K] L)), (cocycle hσ hη) (α * β
enter [2, 2, 2, x]
rw [← AlgEquiv.mul_apply, ← pow_add, H]
rw [← prod_range_add (fun (n : ℕ) ↦ (σ ^ n) (ηu hη)) (a % orderOf σ) (b % orderOf σ)]
simpa using aux1 hσ hη (by simp)
simpa using aux2 hσ hη (by simp)

lemma is_cocycle : IsMulOneCocycle (cocycle hσ hη) := by
intro α β
Expand Down
2 changes: 1 addition & 1 deletion FltRegular/NumberTheory/Hilbert92.lean
Original file line number Diff line number Diff line change
Expand Up @@ -227,7 +227,7 @@ lemma corollary [Module A G] (S : systemOfUnits p G r) (hs : S.IsFundamental) (a
simp only [smul_smul, Finsupp.ofSupportFinite_coe, add_smul, b', b]
congr 1
· rw [mul_comm]
· rw [← intCast_smul (k := A), smul_smul]
· rw [← Int.cast_smul_eq_nsmul (R := A), smul_smul]
· simp

end systemOfUnits.IsFundamental
Expand Down
2 changes: 1 addition & 1 deletion FltRegular/NumberTheory/SystemOfUnits.lean
Original file line number Diff line number Diff line change
Expand Up @@ -79,7 +79,7 @@ lemma existence' [Module A G] {R : ℕ} (S : systemOfUnits p G R) (hR : R < r) :
replace hy := congr_arg (f • ·) hy
simp only at hy
rw [smul_zero, smul_add, smul_smul, mul_comm f,
← Hf, ← eq_neg_iff_add_eq_zero, intCast_smul] at hy
← Hf, ← eq_neg_iff_add_eq_zero, Int.cast_smul_eq_nsmul] at hy
apply hg _ h0
rw [hy]
exact Submodule.neg_mem _ (Submodule.smul_mem _ _ y.2)
Expand Down
10 changes: 5 additions & 5 deletions lake-manifest.json
Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@
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"scope": "leanprover-community",
"rev": "d2b1546c5fc05a06426e3f6ee1cb020e71be5592",
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"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand All @@ -25,7 +25,7 @@
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"scope": "leanprover-community",
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"manifestFile": "lake-manifest.json",
"inputRev": "master",
Expand All @@ -35,10 +35,10 @@
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"scope": "leanprover-community",
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"name": "proofwidgets",
"manifestFile": "lake-manifest.json",
"inputRev": "v0.0.39",
"inputRev": "v0.0.40",
"inherited": true,
"configFile": "lakefile.lean"},
{"url": "https://github.com/leanprover/lean4-cli",
Expand All @@ -65,7 +65,7 @@
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"inputRev": null,
Expand Down

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