Theorems · Theorem · several complex variables
FormalMultilinearSeries.comp_id
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
(p : FormalMultilinearSeries 𝕜 E F) (x : E), p.comp (FormalMultilinearSeries.id 𝕜 E x) = p- Defined in
- Mathlib.Analysis.Analytic.Composition
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.univproof · cited by 3,473
- ContinuousMultilinearMapproof · cited by 1,016
- FormalMultilinearSeriesstatement and proof · cited by 615
- zero_applyproof · cited by 251
- Compositionproof · cited by 138
- Finset.sum_eq_singleproof · cited by 98
- Composition.lengthproof · cited by 92
- ContinuousMultilinearMap.extproof · cited by 62
Cited by1
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.leftInv_eq_rightInvproof · cited by 1