Theorems · Theorem · logic and foundations
Cardinal.one_lt_aleph0
1 < 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Nat.cast_oneproof · cited by 2,501
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.natCast_lt_aleph0proof · cited by 47
Cited by20
Results whose statement or proof uses this declaration.
- Cardinal.one_le_aleph0proof · cited by 6
- Cardinal.pow_leproof · cited by 5
- Order.cof_lt_aleph0_iffproof · cited by 4
- Cardinal.mk_Ioi_realproof · cited by 3
- finrank_le_oneproof · cited by 2
- Cardinal.ciSup_mulproof · cited by 2
- Collinear.finiteDimensional_vectorSpanproof · cited by 2
- MeasurableSpace.cardinal_generateMeasurableRec_leproof · cited by 1
- Cardinal.add_one_lt_of_ltproof · cited by 1
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1
- LinearEquiv.mem_dilatransvections_iff_finrankproof · cited by 1
- Ordinal.nfp_lt_ordproof · cited by 1