Theorems · Theorem · group theory
Equiv.Perm.support_swap_mul_swap
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {x y z : α},
[x, y, z].Nodup → (Equiv.swap x y * Equiv.swap y z).support = {x, y, z}- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- le_antisymmproof · cited by 2,068
- Equiv.Permstatement · cited by 1,375
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.swapstatement and proof · cited by 197
- Equiv.swap_apply_leftproof · cited by 44
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- Equiv.swap_apply_rightproof · cited by 31
- Finset.insert_eq_of_memproof · cited by 28
- Finset.union_insertproof · cited by 17
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