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Theorems · Theorem · order theory

IsLowerSet.vadd

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : Preorder α] [IsOrderedAddMonoid α] {s : Set α} {a : α},
  IsLowerSet s → IsLowerSet (a +ᵥ s)
Defined in
Mathlib.Algebra.Order.UpperLower
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
AddCommGroupPreorderIsOrderedAddMonoid
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Around this declaration

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

Set.OrdConnected.vadd · cited by 0OrdConnected.vaddSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupPreorder · cited by 7952PreorderHVAdd.hVAdd · cited by 1820HVAdd.hVAddIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidSet.vaddSet · cited by 403Set.vaddSetIsLowerSet · cited by 167IsLowerSetOrderIso.addLeft · cited by 18OrderIso.addLeftIsLowerSet.image · cited by 2IsLowerSet.imageIsLowerSet.vaddCITED BYCITES

Cites9

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Cited by1

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