Theorems · Theorem · order theory
Finset.ciSup_union
∀ {ι : Type u_1} {α : Type u_2} [inst : ConditionallyCompleteLinearOrderBot α] [inst_1 : DecidableEq ι] {f : ι → α}
{s t : Finset ι}, ⨆ x ∈ s ∪ t, f x = max (⨆ x ∈ s, f x) (⨆ x ∈ t, f x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- BddAboveproof · cited by 620
- Finset.supproof · cited by 530
- iSup_congr_Propproof · cited by 247
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- ciSup_of_emptyproof · cited by 23
- ciSup_uniqueproof · cited by 16
- ciSup_sup_eqproof · cited by 3
- ciSup_or'proof · cited by 1
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