Theorems · Theorem · logic and foundations
Cardinal.natCast_le_toENat
∀ {c : Cardinal.{u}} {n : ℕ}, ↑n ≤ Cardinal.toENat c ↔ ↑n ≤ c- Defined in
- Mathlib.SetTheory.Cardinal.ENat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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.
- DFunLike.coestatement and proof · cited by 62,936
- ENatstatement and proof · cited by 4,985
- Cardinalstatement and proof · cited by 2,598
- OrderRingHomstatement · cited by 132
- Cardinal.toENatstatement and proof · cited by 92
- Cardinal.natCast_le_aleph0proof · cited by 20
- Cardinal.toENat_natproof · cited by 4
- Cardinal.toENat_le_iff_of_le_aleph0proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.ofNat_le_toENatproof · cited by 1
- Cardinal.natCast_eq_toENat_iffproof · cited by 0
- Cardinal.one_le_toENatproof · cited by 0