Theorems · Theorem · order theory
Finite.ciSup_sup
∀ {α : Type u_1} {ι : Type u_2} [Finite ι] [inst : ConditionallyCompleteLattice α] [Nonempty ι] {f : ι → α} {a : α},
(⨆ i, f i) ⊔ a = ⨆ i, f i ⊔ a- Defined in
- Mathlib.Data.Fintype.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- ConditionallyCompleteLatticestatement and proof · cited by 364
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Classical.arbitraryproof · cited by 161
- sup_leproof · cited by 159
- ciSup_leproof · cited by 56
- Finite.le_ciSup_of_leproof · cited by 17
- sup_le_sup_rightproof · cited by 14
- Finite.le_ciSupproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Finite.ciInf_infproof · cited by 0