Theorems · Theorem · logic and foundations
HasCardinalLT.exists_regular_cardinal_forall
∀ {ι : Type v} (X : ι → Type u) [Small.{w, v} ι] [∀ (i : ι), Small.{w, u} (X i)],
∃ κ, κ.IsRegular ∧ ∀ (i : ι), HasCardinalLT (X i) κFor any w-small family X : ι → Type u of w-small types, there exists
a regular cardinal κ : Cardinal.{w} such that HasCardinalLT (X i) κ for all i : ι.
- Defined in
- Mathlib.SetTheory.Cardinal.HasCardinalLT
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Smallstatement and proof · cited by 369
- Cardinal.IsRegularstatement and proof · cited by 282
- HasCardinalLTstatement and proof · cited by 99
- sigma_mk_injectiveproof · cited by 27
- HasCardinalLT.of_injectiveproof · cited by 9
- HasCardinalLT.exists_regular_cardinalproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.presentableproof · cited by 0