Theorems · Theorem · logic and foundations
Cardinal.toENat_eq_natCast
∀ {c : Cardinal.{u}} {n : ℕ}, Cardinal.toENat c = ↑n ↔ c = ↑n- Defined in
- Mathlib.SetTheory.Cardinal.ENat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- ENatstatement · cited by 4,985
- Cardinalstatement and proof · cited by 2,598
- OrderRingHomstatement · cited by 132
- Cardinal.toENatstatement · cited by 92
- Cardinal.toENatAux_eq_natproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.toNat_eq_iffproof · cited by 5
- Cardinal.toENat_eq_zeroproof · cited by 1
- Cardinal.toENat_eq_oneproof · cited by 0
- Module.length_of_free_of_finiteproof · cited by 0
- Cardinal.toENat_eq_natproof · cited by 0
- Cardinal.toENat_eq_ofNatproof · cited by 0