Project-declaredLean 4.32.0 · mathlib@249c48c2

Number Field Adele Ring add Equiv Add Haar Char mul Right unit eq one

NumberField.AdeleRing.addEquivAddHaarChar_mulRight_unit_eq_one

number theory arithmetic geometry Fermat's Last Theorem adele ring

Plain-language statement

Right multiplication by an element of Bˣ on B ⊗ 𝔸_K does not scale additive Haar measure.

Exact Lean statement

lemma NumberField.AdeleRing.addEquivAddHaarChar_mulRight_unit_eq_one
    [MeasurableSpace (B ⊗[K] AdeleRing (𝓞 K) K)] [BorelSpace (B ⊗[K] AdeleRing (𝓞 K) K)]
    (b : Bˣ) :
    addEquivAddHaarChar
      (ContinuousAddEquiv.mulRight
        (Units.map Algebra.TensorProduct.includeLeftRingHom.toMonoidHom b :
      (B ⊗[K] AdeleRing (𝓞 K) K)ˣ)) = 1

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma NumberField.AdeleRing.addEquivAddHaarChar_mulRight_unit_eq_one    [MeasurableSpace (B ⊗[K] AdeleRing (𝓞 K) K)] [BorelSpace (B ⊗[K] AdeleRing (𝓞 K) K)]    (b : Bˣ) :    addEquivAddHaarChar      (ContinuousAddEquiv.mulRight        (Units.map Algebra.TensorProduct.includeLeftRingHom.toMonoidHom b :      (B ⊗[K] AdeleRing (𝓞 K) K)ˣ)) = 1 := by  convert! addHaarScalarFactor_tensor_adeles_eq_one K B (LinearEquiv.mulRight K b)  ext c  change _ = (ContinuousLinearEquiv.baseChange K _ _ _ _) c  induction c with  | zero => simp  | tmul x y => simp [LinearEquiv.mulRight]  | add x y hx hy => simp_all [add_mul]

Project: Fermat's Last Theorem
License: Apache-2.0
Commit: 8dd808888295
Source: FLT/HaarMeasure/HaarChar/AdeleRing.lean:241-254

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