Theorems · Theorem · logic and foundations
Cardinal.toNat_natCast
∀ (n : ℕ), Cardinal.toNat ↑n = n
- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 19 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.
Cites5
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 · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.toNatstatement · cited by 153
- Cardinal.toNat_ofENatproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Module.finrank_eq_card_chooseBasisIndexproof · cited by 21
- Module.finrank_eq_of_rank_eqproof · cited by 13
- Cardinal.cast_toNat_of_lt_aleph0proof · cited by 9
- Cardinal.mk_toNat_eq_cardproof · cited by 6
- Module.finrank_piproof · cited by 5
- Cardinal.toNat_strictMonoOnproof · cited by 5
- Module.lt_rank_of_lt_finrankproof · cited by 3
- Module.finrank_le_of_rank_leproof · cited by 3
- Matrix.rank_diagonalproof · cited by 3
- Cardinal.toNat_addproof · cited by 2
- Cardinal.toNat_ofNatproof · cited by 2
- Submodule.FG.exists_span_set_encard_eq_spanFinrankproof · cited by 1