Theorems · Theorem · order theory
WithTop.add_lt_add_iff_left
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [inst_1 : LT α] [AddLeftStrictMono α] [AddLeftReflectLT α],
x ≠ ⊤ → (x + y < x + z ↔ y < z)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 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
- AddLeftStrictMonostatement and proof · cited by 203
- AddLeftReflectLTstatement and proof · cited by 33
- lt_of_add_lt_add_leftproof · cited by 9
- WithTop.add_lt_add_leftproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.add_lt_add_iff_leftproof · cited by 2
- ENat.add_lt_add_iff_leftproof · cited by 0