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Theorems · Theorem · order theory

biSup_const

∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {a : α} {s : Set β}, s.Nonempty → ⨆ i ∈ s, a = a
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.biUnion_const · cited by 4Set.biUnion_constFilter.sup_limsup · cited by 2Filter.sup_limsupSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.Nonempty · cited by 2627Set.NonemptyiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeSet.nonempty_coe_sort · cited by 23Set.nonempty_coe_sortiSup_subtype'' · cited by 18iSup_subtype''iSup_const · cited by 13iSup_constbiSup_constCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.