Theorems · Theorem · logic and foundations
Cardinal.toENatAux_le_nat
∀ {x : Cardinal.{u_1}} {n : ℕ}, x.toENatAux ≤ ↑n ↔ x ≤ ↑n- Defined in
- Mathlib.SetTheory.Cardinal.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LT.lt.trans_leproof · cited by 678
- Cardinal.aleph0proof · cited by 521
- lt_or_geproof · cited by 182
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.toENatAuxstatement · cited by 8
- Cardinal.toENatAux_natproof · cited by 4
- Cardinal.toENatAux_eq_topproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.toENat_le_natCastproof · cited by 6