Theorems · Theorem · combinatorics
Finset.insert_erase_invOn
∀ {α : Type u_1} [inst : DecidableEq α] {a : α}, Set.InvOn (insert a) (fun s => s.erase a) {s | a ∈ s} {s | a ∉ s}- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 57 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Set.ofPredstatement · cited by 6,101
- Finset.erasestatement · cited by 455
- Finset.insert_eraseproof · cited by 65
- Set.InvOnstatement · cited by 26
- Finset.erase_insertproof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- Finset.sum_powerset_insertproof · cited by 2
- sum_collapseproof · cited by 1
- Finset.prod_powerset_insertproof · cited by 1
- Finset.memberSubfamily_image_insertproof · cited by 0
- Finset.card_le_card_shattererproof · cited by 0
- Finset.pairwiseDisjoint_pair_insertproof · cited by 0