Theorems · Theorem · combinatorics
Fintype.card_eq_one_iff
∀ {α : Type u_1} [inst : Fintype α], Fintype.card α = 1 ↔ ∃ x, ∀ (y : α), y = x- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 62 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Equiv.symmproof · cited by 3,681
- Fintype.cardstatement and proof · cited by 1,386
- Equiv.injectiveproof · cited by 464
- Fintype.card_eqproof · cited by 19
- Fintype.card_unitproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- Fintype.card_le_one_iffproof · cited by 4
- Fintype.card_eq_one_iff_nonempty_uniqueproof · cited by 3
- RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_leproof · cited by 2
- card_classGroup_eq_one_iffproof · cited by 2
- AffineIndependent.existsUnique_dist_eqproof · cited by 1
- Submonoid.card_botproof · cited by 1
- AddSubmonoid.card_botproof · cited by 1
- Fintype.card_embedding_eqproof · cited by 1
- card_classGroup_eq_oneproof · cited by 1
- Fintype.card_eq_one_of_forall_eqproof · cited by 1
- Field.primitive_element_iff_algHom_eq_of_evalproof · cited by 1