Mathlib Map

Theorems · Theorem · order theory

IsUpperSet.vadd

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

Around this declaration

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

IsUpperSet.add_left · cited by 3IsUpperSet.add_leftSet.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.vaddSetIsUpperSet · cited by 148IsUpperSetOrderIso.addLeft · cited by 18OrderIso.addLeftIsUpperSet.image · cited by 2IsUpperSet.imageIsUpperSet.vaddCITED BYCITES

Cites9

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.