Theorems · Theorem · logic and foundations
Set.eq_insert_of_ncard_eq_succ
∀ {α : Type u_1} {s : Set α} {n : ℕ}, s.ncard = n + 1 → ∃ a t, a ∉ t ∧ insert a t = s ∧ t.ncard = n- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Finset.cardproof · cited by 2,327
- Set.Finiteproof · cited by 1,814
- Set.Finite.toFinsetproof · cited by 351
- Set.ncardstatement and proof · cited by 344
- LT.lt.trans_eqproof · cited by 65
- Set.ncard_eq_toFinset_cardproof · cited by 21
- Set.ncard_coe_finsetproof · cited by 15
- Finset.card_eq_succproof · cited by 7
- Set.finite_of_ncard_posproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.ncard_eq_succproof · cited by 0