Theorems · Theorem · order theory

Set.AddAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd

∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsCancelAdd α] [AddLeftMono α]
  [AddRightStrictMono α] (s t : Set α) (a : α) {x y : ↑(s.antidiagonal t a)}, (↑x).1 ≤ (↑y).1 → (↑x).2 ≤ (↑y).2 → x = y

Defined in

Mathlib.Data.Set.MulAntidiagonal

Cited by

1 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsCancelAddAddLeftMonoAddRightStrictMono