Theorems · Theorem · order theory
WithTop.le_of_add_le_add_left
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [inst_1 : LE α] [AddLeftReflectLE α], x ≠ ⊤ → x + y ≤ x + z → y ≤ z- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- AddLEAddLeftReflectLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- WithTop.someproof · cited by 1,128
- AddLeftReflectLEstatement and proof · cited by 119
- WithTop.recTopCoeproof · cited by 107
- WithTop.add_topproof · cited by 18
- le_of_add_le_add_leftproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- WithTop.addLECancellable_of_ne_topproof · cited by 4
- ENNReal.le_of_add_le_add_leftproof · cited by 2
- WithTop.add_le_add_iff_leftproof · cited by 2