Theorems · Theorem · logic and foundations
Cardinal.toNat_lt_iff_lt_of_lt_aleph0
∀ {c d : Cardinal.{u}}, c < Cardinal.aleph0 → d < Cardinal.aleph0 → (Cardinal.toNat c < Cardinal.toNat d ↔ c < d)- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Cardinalstatement and proof · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.toNatstatement · cited by 153
- StrictMonoOn.lt_iff_ltproof · cited by 14
- Cardinal.toNat_strictMonoOnproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Module.lt_rank_of_lt_finrankproof · cited by 3
- Module.finrank_lt_of_rank_ltproof · cited by 0
- FiniteDimensional.finrank_lt_iff_rank_ltproof · cited by 0