Theorems · Definition · group theory
List.formPerm
{α : Type u_1} → [DecidableEq α] → List α → Equiv.Perm αA list l : List α can be interpreted as an Equiv.Perm α where each element in the list
is permuted to the next one, defined as formPerm. When we have that Nodup l,
we prove that Equiv.Perm.support (formPerm l) = l.toFinset, and that
formPerm l is rotationally invariant, in formPerm_rotate.
- Defined in
- Mathlib.GroupTheory.Perm.List
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.Permstatement · cited by 1,375
- Equiv.swapproof · cited by 197
Cited by55
Results whose statement or proof uses this declaration.
- Cycle.formPermproof · cited by 13
- List.formPerm_apply_of_notMemstatement · cited by 7
- List.isCycle_formPermstatement and proof · cited by 6
- List.formPerm_apply_getElemstatement · cited by 6
- List.support_formPerm_le'statement · cited by 5
- List.formPerm_pow_apply_getElemstatement and proof · cited by 4
- List.mem_of_formPerm_apply_nestatement and proof · cited by 4
- List.support_formPerm_of_nodupstatement and proof · cited by 4
- List.formPerm_apply_mem_eq_self_iffstatement · cited by 3
- List.formPerm_apply_mem_ne_self_iffstatement and proof · cited by 3
- Equiv.Perm.exists_with_cycleType_iffproof · cited by 2
- List.Nodup.isCycleOn_formPermstatement and proof · cited by 2