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Theorems · Theorem · logic and foundations

Cardinal.natCast_le_aleph0

∀ {n : ℕ}, ↑n ≤ Cardinal.aleph0
Defined in
Mathlib.SetTheory.Cardinal.Basic
Cited by
20 results in Mathlib
Foundations
Depth 78 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.

Cardinal.power_self_eq · cited by 6Cardinal.power_self_eqCardinal.add_eq_self · cited by 4Cardinal.add_eq_selfCardinal.natCast_le_toENat · cited by 3Cardinal.natCast_le_toENatCardinal.aleph0_add_nat · cited by 2Cardinal.aleph0_add_natCardinal.aleph0_le · cited by 2Cardinal.aleph0_leField.Emb.cardinal_eq_two_pow_rank · cited by 2Emb.cardinal_eq_two_pow_r…LinearMap.exists_isNilRegular · cited by 2LinearMap.exists_isNilReg…strongRankCondition_iff_forall_rank_lt_aleph0 · cited by 1strongRankCondition_iff_f…Cardinal.add_nat_eq · cited by 1Cardinal.add_nat_eqOrdinal.card_opow_le · cited by 1Ordinal.card_opow_leCardinal.nat_power_eq · cited by 1Cardinal.nat_power_eqCardinal.preBeth_omega · cited by 1Cardinal.preBeth_omegaFreeGroup.injective_lift_of_ping_pong · cited by 0FreeGroup.injective_lift_…Cardinal.natCast_le_toENat_iff · cited by 0Cardinal.natCast_le_toENa…Cardinal.mk_freeAddGroup · cited by 0Cardinal.mk_freeAddGroupCardinal · cited by 2598CardinalLT.lt.le · cited by 2189lt.leCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.natCast_lt_aleph0 · cited by 47Cardinal.natCast_lt_aleph0Cardinal.natCast_le_aleph0CITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.