Theorems · Theorem · logic and foundations
Cardinal.eq_one_iff_unique
∀ {α : Type u_1}, Cardinal.mk α = 1 ↔ Subsingleton α ∧ Nonempty α- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- le_antisymm_iffproof · cited by 62
- Iff.andproof · cited by 33
- Cardinal.one_le_iff_ne_zeroproof · cited by 14
- Cardinal.mk_ne_zero_iffproof · cited by 11
- Cardinal.le_one_iff_subsingletonproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Subalgebra.eq_bot_of_rank_le_oneproof · cited by 3
- Cardinal.toNat_eq_one_iff_uniqueproof · cited by 1
- Cardinal.mk_set_eq_one_iffproof · cited by 1