Theorems · Definition · group theory
Fin.cycleIcc
{n : ℕ} → Fin n → Fin n → Equiv.Perm (Fin n)cycleIcc i j is the cycle (i i+1 ... j) leaving (0 ... i-1) and (j+1 ... n-1)
unchanged when i < j and returning the dummy value id when i > j.
In other words, it rotates elements in [i, j] one step to the right.
- Defined in
- Mathlib.GroupTheory.Perm.Fin
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 65 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.
- Equiv.Permstatement · cited by 1,375
- Fin.cycleRangeproof · cited by 35
- Equiv.Perm.extendDomainproof · cited by 34
- Function.Embedding.toEquivRangeproof · cited by 23
- Fin.natAdd_castLEEmbproof · cited by 11
- Fin.sub_val_lt_subproof · cited by 8
Cited by22
Results whose statement or proof uses this declaration.
- Fin.cycleIcc_def_lestatement · cited by 5
- Fin.cycleIcc_of_le_of_lestatement · cited by 5
- Fin.cycleIcc_def_gt'statement · cited by 3
- Fin.cycleIcc_gestatement and proof · cited by 3
- Fin.cycleIcc_of_gtstatement · cited by 3
- Fin.cycleIcc_of_ltstatement · cited by 2
- Fin.cycleIcc_to_cycleRangestatement · cited by 2
- Fin.cycleIcc_def_gtstatement · cited by 1
- Fin.cycleIcc_eqstatement and proof · cited by 1
- Fin.cycleIcc_of_ge_of_ltstatement · cited by 1
- Fin.cycleIcc_of_laststatement · cited by 1
- Fin.sign_cycleIcc_of_eqstatement · cited by 1