Theorems · Theorem · order theory

add_lowerClosure

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

Defined in

Mathlib.Algebra.Order.UpperLower

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupPreorderIsOrderedAddMonoid