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Theorems · Theorem · order theory

upperClosure_vadd

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : Preorder α] [inst_2 : IsOrderedAddMonoid α] (s : Set α) (a : α),
  upperClosure (a +ᵥ s) = a +ᵥ upperClosure s
Defined in
Mathlib.Algebra.Order.UpperLower
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPreorderIsOrderedAddMonoid
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Around this declaration

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

add_upperClosure · cited by 2add_upperClosureSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupPreorder · cited by 7952PreorderHVAdd.hVAdd · cited by 1820HVAdd.hVAddIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidSet.vaddSet · cited by 403Set.vaddSetUpperSet · cited by 245UpperSetupperClosure · cited by 84upperClosureOrderIso.addLeft · cited by 18OrderIso.addLeftupperClosure_image · cited by 3upperClosure_imageupperClosure_vaddCITED BYCITES

Cites10

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Cited by1

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