Theorems · Theorem · logic and foundations
Set.encard_le_coe_iff
∀ {α : Type u_1} {s : Set α} {k : ℕ}, s.encard ≤ ↑k ↔ s.Finite ∧ ∃ n₀, s.encard = ↑n₀ ∧ n₀ ≤ k- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Finitestatement and proof · cited by 1,814
- Set.encardstatement and proof · cited by 327
- Nat.cast_leproof · cited by 159
- Set.finite_of_encard_le_coeproof · cited by 5
- ENat.le_natCast_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.encard_le_coe_iff_finite_ncard_leproof · cited by 0