Theorems · Theorem · logic and foundations
Set.encard_eq_add_one_iff
∀ {α : Type u_1} {s : Set α} {k : ℕ∞}, s.encard = k + 1 ↔ ∃ a t, a ∉ t ∧ insert a t = s ∧ t.encard = k- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- ENatstatement and proof · cited by 4,985
- Set.encardstatement and proof · cited by 327
- Set.insert_eq_of_memproof · cited by 118
- Set.insert_sdiff_singletonproof · cited by 28
- Set.encard_insert_of_notMemproof · cited by 17
- ENat.one_ne_topproof · cited by 15
- AddLECancellable.add_tsub_cancel_rightproof · cited by 9
- ENat.addLECancellable_of_ne_topproof · cited by 9
- Set.nonempty_of_encard_ne_zeroproof · cited by 5
- Set.encard_sdiff_singleton_of_memproof · cited by 3
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