Theorems · Theorem · logic and foundations
Cardinal.IsRegular.aleph0_le
∀ {c : Cardinal.{u_1}}, c.IsRegular → Cardinal.aleph0 ≤ cA regular cardinal is infinite.
- Defined in
- Mathlib.SetTheory.Cardinal.Regular
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.aleph0statement · cited by 521
- Cardinal.IsRegularstatement and proof · cited by 282
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.isFiltered_of_isCardinalFilteredproof · cited by 18
- CategoryTheory.IsCardinalFiltered.coeq_conditionproof · cited by 7
- Cardinal.IsRegular.posproof · cited by 2
- Cardinal.sum_lt_lift_of_isRegularproof · cited by 2
- CategoryTheory.CardinalDirectedPoset.propSetWithTop_pairproof · cited by 2
- Cardinal.derivFamily_lt_ord_liftproof · cited by 2
- Cardinal.IsRegular.nat_ltproof · cited by 2
- Cardinal.card_iUnion_lt_iff_forall_of_isRegularproof · cited by 1
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directedproof · cited by 1
- CategoryTheory.CardinalDirectedPoset.propSet_singletonproof · cited by 1