Theorems · Theorem · order theory

Set.Ioc_add_Ico_subset

∀ {α : Type u_1} [inst : Add α] [inst_1 : PartialOrder α] [AddLeftStrictMono α] [AddRightStrictMono α] (a b c d : α),
  Set.Ioc a b + Set.Ico c d ⊆ Set.Ioo (a + c) (b + d)

Defined in

Mathlib.Algebra.Order.Group.Pointwise.Interval

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddPartialOrderAddLeftStrictMonoAddRightStrictMono