Theorems · Theorem · logic and foundations
Cardinal.mk_singleton
∀ {α : Type u} (x : α), Cardinal.mk ↑{x} = 1- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.mk_eq_oneproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- rank_subsingletonproof · cited by 19
- Order.cof_eq_one_iffproof · cited by 4
- Cardinal.mk_insertproof · cited by 3
- Cardinal.mk_Ioi_realproof · cited by 3
- HahnSeries.cardSupp_single_leproof · cited by 3
- MeasurableSpace.cardinal_generateMeasurableRec_leproof · cited by 1
- HahnSeries.cardSupp_single_of_neproof · cited by 1
- Subalgebra.rank_botproof · cited by 1
- Cardinal.mk_subset_mk_lt_cofproof · cited by 0