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Theorems · Theorem · several complex variables

FormalMultilinearSeries.id_apply_of_one_lt

∀ (𝕜 : Type u_1) (E : Type u_2) [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] (x : E) {n : ℕ}, 1 < n → FormalMultilinearSeries.id 𝕜 E x n = 0

For n ≠ 1, the n-th coefficient of id 𝕜 E is zero, by definition.

Defined in
Mathlib.Analysis.Analytic.Composition
Cited by
4 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FormalMultilinearSeries.leftInv_comp · cited by 2FormalMultilinearSeries.l…FormalMultilinearSeries.comp_id · cited by 1FormalMultilinearSeries.c…FormalMultilinearSeries.comp_rightInv · cited by 1FormalMultilinearSeries.c…FormalMultilinearSeries.id_comp · cited by 1FormalMultilinearSeries.i…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapFormalMultilinearSeries.id · cited by 10FormalMultilinearSeries.idFormalMultilinearSeries.id_ap…CITED BYCITES

Cites5

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Cited by4

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