Theorems · Theorem · logic and foundations
Cardinal.mk_eq_one
∀ (α : Type u) [Subsingleton α] [Nonempty α], Cardinal.mk α = 1
- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubsingletonNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Uniqueproof · cited by 400
- Equiv.cardinal_eqproof · cited by 35
- nonempty_uniqueproof · cited by 11
- Equiv.ofUniqueproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- Cardinal.lift_oneproof · cited by 33
- Cardinal.mk_singletonproof · cited by 9
- Ordinal.card_oneproof · cited by 6
- Cardinal.power_zeroproof · cited by 4
- Cardinal.mk_punitproof · cited by 2
- Field.Emb.cardinal_separableClosureproof · cited by 2
- Cardinal.prod_eq_of_fintypeproof · cited by 2
- FreeAlgebra.cardinalMk_eq_oneproof · cited by 1
- Cardinal.mk_optionproof · cited by 1
- Polynomial.cardinalMk_le_maxproof · cited by 1
- Cardinal.one_powerproof · cited by 0
- Cardinal.sum_zero_powproof · cited by 0