Theorems · Theorem · order theory
WithTop.add_le_add_iff_left
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [inst_1 : LE α] [AddLeftMono α] [AddLeftReflectLE α],
x ≠ ⊤ → (x + y ≤ x + z ↔ y ≤ z)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- WithTopstatement and proof · cited by 3,754
- AddLeftMonostatement and proof · cited by 687
- AddLeftReflectLEstatement and proof · cited by 119
- add_le_add_rightproof · cited by 37
- WithTop.le_of_add_le_add_leftproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.add_le_add_iff_leftproof · cited by 0
- ENat.add_le_add_iff_leftproof · cited by 0