Theorems · Theorem · order theory
Equiv.bijOn_swap
∀ {α : Type u_1} {s : Set α} [inst : DecidableEq α] {a b : α}, a ∈ s → b ∈ s → Set.BijOn (⇑(Equiv.swap a b)) s s- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 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.
Cites11
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 and proof · cited by 53,352
- Equiv.Permstatement · cited by 1,375
- eq_or_neproof · cited by 1,117
- Equiv.swapstatement and proof · cited by 197
- Set.BijOnstatement · cited by 168
- Equiv.swap_apply_leftproof · cited by 44
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- Equiv.swap_apply_rightproof · cited by 31
- Equiv.swap_selfproof · cited by 18
- Equiv.bijOnproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCycleOn_swapproof · cited by 0