Theorems · Theorem · order theory
Set.MulAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd
∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [IsCancelMul α] [MulLeftMono α] [MulRightStrictMono α]
(s t : Set α) (a : α) {x y : ↑(s.mulAntidiagonal 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- CommMonoidstatement and proof · cited by 2,264
- LT.lt.neproof · cited by 872
- MulLeftMonostatement and proof · cited by 410
- MulRightStrictMonostatement and proof · cited by 108
- IsCancelMulstatement and proof · cited by 32
- LE.le.eq_of_not_ltproof · cited by 25
- mul_lt_mul_of_lt_of_leproof · cited by 18
- Set.mulAntidiagonalstatement and proof · cited by 11
- Set.mem_mulAntidiagonalproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.MulAntidiagonal.finite_of_isPWOproof · cited by 1