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Theorems · Theorem · order theory

bddBelow_insert

∀ {α : Type u_1} [inst : Preorder α] [IsCodirectedOrder α] {s : Set α} {a : α}, BddBelow (insert a s) ↔ BddBelow s

Adding a point to a set preserves its boundedness below.

Defined in
Mathlib.Order.Bounds.Basic
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
PreorderIsCodirectedOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

BddBelow.insert · cited by 1BddBelow.insertSet · cited by 53352SetPreorder · cited by 7952PreorderBddBelow · cited by 401BddBelowIsCodirectedOrder · cited by 95IsCodirectedOrderbddBelow_union · cited by 3bddBelow_unionbddBelow_singleton · cited by 1bddBelow_singletonbddBelow_insertCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.