Theorems · Theorem · logic and foundations
Cardinal.ciSup_add
∀ {ι : Type u} (f : ι → Cardinal.{v}) [Nonempty ι],
BddAbove (Set.range f) → ∀ (c : Cardinal.{v}), (⨆ i, f i) + c = ⨆ i, f i + c- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- add_le_addproof · cited by 666
- BddAbovestatement and proof · cited by 620
- le_imp_le_of_le_of_leproof · cited by 576
- Cardinal.aleph0proof · cited by 521
- lt_or_geproof · cited by 182
- Classical.arbitraryproof · cited by 161
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.ciSup_add_ciSupproof · cited by 3
- Cardinal.add_ciSupproof · cited by 1