Theorems · Theorem · logic and foundations
Cardinal.mk_set_le
∀ {α : Type u} (s : Set α), Cardinal.mk ↑s ≤ Cardinal.mk α- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, 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 and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.mk_subtype_leproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- Cardinal.lift_mk_le_lift_mk_of_injectiveproof · cited by 10
- Cardinal.mk_Ioo_realproof · cited by 5
- Filter.EventuallyConst.of_monotone_of_lt_cofproof · cited by 3
- Cardinal.mk_Ioi_realproof · cited by 3
- rank_le_cardproof · cited by 2
- Cardinal.mk_Icc_realproof · cited by 2
- Cardinal.mk_Iio_realproof · cited by 1
- Cardinal.mk_Ioc_realproof · cited by 1
- Cardinal.mk_of_countable_eventually_memproof · cited by 1
- Cardinal.mk_surjective_eq_arrow_of_lift_leproof · cited by 1
- Cardinal.mk_Ico_realproof · cited by 1
- Cardinal.card_le_of_finsetproof · cited by 0