Theorems · Definition · combinatorics
Composition.boundary
{n : ℕ} → (c : Composition n) → Fin (c.length + 1) ↪o Fin (n + 1)The i-th boundary of a composition, i.e., the leftmost point of the i-th block. We include
a virtual point at the right of the last block, to make for a nice equiv with
CompositionAsSet n.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- OrderEmbeddingstatement · cited by 619
- Compositionstatement and proof · cited by 138
- Composition.lengthstatement and proof · cited by 92
- Composition.sizeUpToproof · cited by 26
- OrderEmbedding.ofStrictMonoproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Composition.boundariesproof · cited by 5
- Composition.card_boundaries_eq_succ_lengthproof · cited by 3
- Composition.orderEmbOfFin_boundariesstatement and proof · cited by 1
- Composition.boundary_laststatement · cited by 0
- Composition.boundary_zerostatement · cited by 0
- Composition.toCompositionAsSet_blocksproof · cited by 0