Mathlib Map

Theorems · Theorem · combinatorics

List.length_splitWrtComposition

∀ {n : ℕ} {α : Type u_1} (l : List α) (c : Composition n), (l.splitWrtComposition c).length = c.length

When one splits a list along a composition c, the number of sublists thus created is c.length.

Defined in
Mathlib.Combinatorics.Enumerative.Composition
Cited by
3 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Composition.length_gather · cited by 4Composition.length_gatherComposition.length_sigmaCompositionAux · cited by 3Composition.length_sigmaC…Composition.sizeUpTo_sizeUpTo_add · cited by 1Composition.sizeUpTo_size…Composition · cited by 138CompositionComposition.length · cited by 92Composition.lengthComposition.blocks · cited by 49Composition.blocksList.splitWrtComposition · cited by 12List.splitWrtCompositionList.length_splitWrtCompositionAux · cited by 1List.length_splitWrtCompo…List.length_splitWrtCompositi…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.