Theorems · Theorem · logic and foundations
Cardinal.le_mk_iff_exists_set
∀ {c : Cardinal.{u}} {α : Type u}, c ≤ Cardinal.mk α ↔ ∃ p, Cardinal.mk ↑p = c- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Equiv.ofInjectiveproof · cited by 64
- Equiv.cardinal_eqproof · cited by 35
- Cardinal.inductionOnproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.lt_aleph0proof · cited by 19
- Cardinal.infinite_pigeonhole_cardproof · cited by 4
- Cardinal.le_mk_iff_exists_subsetproof · cited by 2
- Cardinal.infinite_pigeonholeproof · cited by 1
- FirstOrder.Language.exists_elementarySubstructure_card_eqproof · cited by 1
- Ordinal.ord_mk_le_typeproof · cited by 0