Theorems · Theorem · logic and foundations
Cardinal.mk_sUnion_le
∀ {α : Type u} (A : Set (Set α)), Cardinal.mk ↑(⋃₀ A) ≤ Cardinal.mk ↑A * ⨆ s, Cardinal.mk ↑↑s- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 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.
Cites8
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
- Cardinalstatement · cited by 2,598
- iSupstatement and proof · cited by 2,415
- Cardinal.mkstatement and proof · cited by 942
- Set.sUnionstatement · cited by 392
- Set.sUnion_eq_iUnionproof · cited by 26
- Cardinal.mk_iUnion_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.card_iUnion_lt_iff_forall_of_isRegularproof · cited by 1