Theorems · Theorem · combinatorics
Fintype.card_eq_one_iff_nonempty_unique
∀ {α : Type u_1} [inst : Fintype α], Fintype.card α = 1 ↔ Nonempty (Unique α)- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Uniquestatement and proof · cited by 400
- Fintype.card_uniqueproof · cited by 59
- Fintype.card_eq_one_iffproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Module.Invertible.free_iff_linearEquivproof · cited by 3
- Module.Basis.nonempty_unique_index_of_finrank_eq_oneproof · cited by 0
- FinEnum.card_eq_oneproof · cited by 0