Theorems · Theorem · logic and foundations
Set.ncard_lt_card
∀ {α : Type u_1} {s : Set α} [Finite α], s ≠ Set.univ → s.ncard < Nat.card α- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.univstatement and proof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement · cited by 844
- Set.ncardstatement · cited by 344
- Set.toFiniteproof · cited by 174
- Set.ncard_univproof · cited by 21
- Set.ncard_lt_ncardproof · cited by 5
- Set.ssubset_univ_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Set.nonempty_inter_of_le_ncard_add_ncardproof · cited by 1