Mathlib Map

Theorems · Theorem · order theory

Left.min_le_max_of_add_le_add

∀ {α : Type u_1} [inst : Add α] [inst_1 : LinearOrder α] {a b c d : α} [AddLeftStrictMono α] [AddRightMono α],
  a + b ≤ c + d → min a b ≤ max c d
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddLinearOrderAddLeftStrictMonoAddRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

min_le_max_of_add_le_add · cited by 2min_le_max_of_add_le_addLinearOrder · cited by 8572LinearOrderLT.lt.le · cited by 2189lt.leAddRightMono · cited by 367AddRightMononot_le · cited by 328not_leAddLeftStrictMono · cited by 203AddLeftStrictMonoadd_lt_add_of_le_of_lt · cited by 31add_lt_add_of_le_of_ltle_max_iff · cited by 26le_max_iffmin_le_iff · cited by 15min_le_iffLeft.min_le_max_of_add_le_addCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.