Theorems · Theorem · logic and foundations
Cardinal.card_iUnion_lt_iff_forall_of_isRegular
∀ {c : Cardinal.{u}} {ι α : Type u} {t : ι → Set α},
c.IsRegular → Cardinal.mk ι < c → (Cardinal.mk ↑(⋃ i, t i) < c ↔ ∀ (i : ι), Cardinal.mk ↑(t i) < c)- Defined in
- Mathlib.SetTheory.Cardinal.Regular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Set.iUnionstatement · cited by 2,483
- Cardinal.mkstatement and proof · cited by 942
- LE.le.trans_ltproof · cited by 795
- lt_of_le_of_ltproof · cited by 432
- Cardinal.IsRegularstatement and proof · cited by 282
- Cardinal.IsRegular.cof_ordproof · cited by 23
- Cardinal.IsRegular.aleph0_leproof · cited by 22
- Cardinal.mk_range_leproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.card_biUnion_lt_iff_forall_of_isRegularproof · cited by 1