Theorems · Theorem · logic and foundations
Cardinal.natCast_lt_aleph0
∀ {n : ℕ}, ↑n < Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- Nat.cast_add_oneproof · cited by 56
- Cardinal.lift_mk_leproof · cited by 10
- Cardinal.natCast_add_one_le_iffproof · cited by 5
- Cardinal.lift_mk_finproof · cited by 4
Cited by47
Results whose statement or proof uses this declaration.
- Module.rank_lt_aleph0proof · cited by 23
- Cardinal.one_lt_aleph0proof · cited by 20
- Cardinal.natCast_le_aleph0proof · cited by 20
- Cardinal.lt_aleph0proof · cited by 19
- Cardinal.mul_lt_aleph0proof · cited by 6
- Cardinal.add_lt_aleph0proof · cited by 5
- Cardinal.ofENat_strictMonoproof · cited by 4
- Cardinal.power_lt_aleph0proof · cited by 4
- Module.lt_rank_of_lt_finrankproof · cited by 3
- Cardinal.mk_list_eq_mkproof · cited by 3
- LinearIndependent.lt_aleph0_of_finiteproof · cited by 3
- exists_finset_linearIndependent_of_le_rankproof · cited by 3