Theorems · Definition · several complex variables
Composition.sigmaCompositionAux
{n : ℕ} →
(a : Composition n) →
(b : Composition a.length) → (i : Fin (a.gather b).length) → Composition ((a.gather b).blocksFun i)An auxiliary function used in the definition of sigmaEquivSigmaPi below, associating to
two compositions a of n and b of a.length, and an index i bounded by the length of
a.gather b, the subcomposition of a made of those blocks belonging to the i-th block of
a.gather b.
- Defined in
- Mathlib.Analysis.Analytic.Composition
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compositionstatement and proof · cited by 138
- Composition.lengthstatement and proof · cited by 92
- Composition.blocksFunstatement · cited by 52
- Composition.blocksproof · cited by 49
- List.splitWrtCompositionproof · cited by 12
- Composition.gatherstatement and proof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Composition.length_sigmaCompositionAuxstatement · cited by 3
- Composition.sigmaEquivSigmaPiproof · cited by 1
- FormalMultilinearSeries.comp_assocproof · cited by 1
- Composition.blocksFun_sigmaCompositionAuxstatement · cited by 1
- Composition.sizeUpTo_sizeUpTo_addstatement and proof · cited by 1