Theorems · Theorem · group theory
Fin.cycleIcc_def_le
∀ {n : ℕ} {i j : Fin n} (hij : i ≤ j),
i.cycleIcc j = ((j - i).castLT ⋯).cycleRange.extendDomain (Fin.natAdd_castLEEmb ⋯).toEquivRange- Defined in
- Mathlib.GroupTheory.Perm.Fin
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Equiv.Permstatement · cited by 1,375
- Function.Embeddingstatement · cited by 988
- Fin.cycleRangestatement and proof · cited by 35
- Equiv.Perm.extendDomainstatement and proof · cited by 34
- Function.Embedding.toEquivRangestatement and proof · cited by 23
- Fin.cycleIccstatement · cited by 22
- Fin.natAdd_castLEEmbstatement and proof · cited by 11
- Fin.sub_val_lt_substatement and proof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Fin.cycleIcc_of_ltproof · cited by 2
- Fin.cycleIcc_to_cycleRangeproof · cited by 2
- Fin.sign_cycleIcc_of_leproof · cited by 1
- Fin.cycleType_cycleIcc_of_ltproof · cited by 0
- Fin.isCycle_cycleIccproof · cited by 0