Theorems · Definition · logic and foundations
Cardinal.toENat
Cardinal.{u} →+*o ℕ∞Projection from cardinals to ℕ∞. Sends all infinite cardinals to ⊤.
We define this function as a bundled monotone ring homomorphism.
- Defined in
- Mathlib.SetTheory.Cardinal.ENat
- Cited by
- 92 results in Mathlib
- Foundations
- Depth 87 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.
- ENatstatement · cited by 4,985
- Cardinalstatement and proof · cited by 2,598
- OrderRingHomstatement · cited by 132
- Cardinal.toENatAuxproof · cited by 8
- Cardinal.toENatAux_zeroproof · cited by 0
Cited by96
Results whose statement or proof uses this declaration.
- Cardinal.toNatproof · cited by 153
- ENat.cardproof · cited by 89
- Cardinal.toNat_liftproof · cited by 41
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- Matrix.eRankproof · cited by 11
- Cardinal.toENat_liftstatement and proof · cited by 10
- Cardinal.toENat_ofENatstatement · cited by 8
- Submodule.FG.generators_ncardproof · cited by 7
- Cardinal.toENat_le_natCaststatement · cited by 6
- Cardinal.toENat_eq_natCaststatement · cited by 6
- Cardinal.toNat_eq_zeroproof · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesstatement · cited by 5