Theorems · Theorem · order theory

lowerClosure_vadd

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : Preorder α] [inst_2 : IsOrderedAddMonoid α] (s : Set α) (a : α),
  lowerClosure (a +ᵥ s) = a +ᵥ lowerClosure s

Defined in

Mathlib.Algebra.Order.UpperLower

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupPreorderIsOrderedAddMonoid