Theorems · Theorem · combinatorics
Composition.disjoint_range
∀ {n : ℕ} (c : Composition n) {i₁ i₂ : Fin c.length},
i₁ ≠ i₂ → Disjoint (Set.range ⇑(c.embedding i₁)) (Set.range ⇑(c.embedding i₂))The embeddings of different blocks of a composition are disjoint.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Disjointstatement and proof · cited by 2,201
- OrderEmbeddingstatement · cited by 619
- lt_irreflproof · cited by 190
- Compositionstatement and proof · cited by 138
- Disjoint.symmproof · cited by 125
- Ne.lt_or_gtproof · cited by 108
- Composition.lengthstatement and proof · cited by 92
- Composition.blocksFunstatement · cited by 52
- Composition.blocksproof · cited by 49
Cited by1
Results whose statement or proof uses this declaration.
- Composition.mem_range_embedding_iff'proof · cited by 2