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Theorems · Theorem · logic and foundations

Cardinal.cast_toNat_of_lt_aleph0

∀ {c : Cardinal.{u_1}}, c < Cardinal.aleph0 → ↑(Cardinal.toNat c) = c
Defined in
Mathlib.SetTheory.Cardinal.ToNat
Cited by
9 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.finrank_eq_rank · cited by 29Module.finrank_eq_rankNat.cast_card · cited by 3Nat.cast_cardSubmodule.finrank_eq_rank · cited by 3Submodule.finrank_eq_rankexists_finset_linearIndependent_of_le_finrank · cited by 2exists_finset_linearIndep…Cardinal.cast_toNat_eq_iff_lt_aleph0 · cited by 1Cardinal.cast_toNat_eq_if…Cardinal.toNat_eq_iff_of_lt_aleph0 · cited by 1Cardinal.toNat_eq_iff_of_…Cardinal.toNat_eq_of_forall_le_iff · cited by 1Cardinal.toNat_eq_of_fora…Cardinal.natCast_toNat_le · cited by 0Cardinal.natCast_toNat_leCardinal.toNat_apply_of_lt_aleph0 · cited by 0Cardinal.toNat_apply_of_l…DFunLike.coe · cited by 62936DFunLike.coeCardinal · cited by 2598CardinalMonoidWithZeroHom · cited by 704MonoidWithZeroHomCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.toNat · cited by 153Cardinal.toNatCardinal.toNat_natCast · cited by 19Cardinal.toNat_natCastCardinal.cast_toNat_of_lt_ale…CITED BYCITES

Cites6

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Cited by9

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