Theorems · Theorem · logic and foundations
Cardinal.mk_iUnion_le
∀ {α ι : Type u} (f : ι → Set α), Cardinal.mk ↑(⋃ i, f i) ≤ Cardinal.mk ι * ⨆ i, Cardinal.mk ↑(f i)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 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.
Cites9
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
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.mk_iUnion_le_sum_mkproof · cited by 6
- Cardinal.sum_le_mk_mul_iSupproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_sUnion_leproof · cited by 1
- Cardinal.mk_biUnion_leproof · cited by 0