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Theorems · Theorem · order theory

bddAbove_empty

∀ {α : Type u_1} [inst : Preorder α] [Nonempty α], BddAbove ∅
Defined in
Mathlib.Order.Bounds.Basic
Cited by
3 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
PreorderNonempty
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Around this declaration

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

Set.Finite.bddAbove · cited by 19Finite.bddAboveSeminorm.sSup_empty · cited by 1Seminorm.sSup_emptySet.finite_iff_bddAbove_bddBelow · cited by 0Set.finite_iff_bddAbove_b…Set · cited by 53352SetPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptyBddAbove · cited by 620BddAboveupperBounds_empty · cited by 3upperBounds_emptybddAbove_emptyCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.