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Theorems · Theorem · logic and foundations

Cardinal.aleph0_pos

0 < Cardinal.aleph0
Defined in
Mathlib.SetTheory.Cardinal.Order
Cited by
9 results in Mathlib
Foundations
Depth 71 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.isSuccLimit_ord · cited by 11Cardinal.isSuccLimit_ordWType.cardinalMk_le_max_aleph0_of_finite' · cited by 2WType.cardinalMk_le_max_a…Cardinal.IsRegular.pos · cited by 2IsRegular.posCardinal.IsInaccessible.pos · cited by 1IsInaccessible.posFirstOrder.Language.exists_elementarySubstructure_card_eq · cited by 1Language.exists_elementar…Cardinal.beth_pos · cited by 1Cardinal.beth_posCardinal.prime_of_aleph0_le · cited by 1Cardinal.prime_of_aleph0_…Cardinal.aleph_pos · cited by 0Cardinal.aleph_posCardinal.mul_eq_left_iff · cited by 0Cardinal.mul_eq_left_iffCardinal · cited by 2598CardinalCardinal.aleph0 · cited by 521Cardinal.aleph0pos_iff_ne_zero · cited by 180pos_iff_ne_zeroCardinal.aleph0_ne_zero · cited by 6Cardinal.aleph0_ne_zeroCardinal.aleph0_posCITED BYCITES

Cites4

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

Cited by9

Results whose statement or proof uses this declaration.