Theorems · Theorem · order theory
WithTop.add_left_inj
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [IsLeftCancelAdd α], x ≠ ⊤ → (x + y = x + z ↔ y = z)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddIsLeftCancelAdd
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
- WithTop.someproof · cited by 1,128
- IsLeftCancelAddstatement and proof · cited by 72
- IsAddLeftRegular.allproof · cited by 5
- IsAddLeftRegular.withTopproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1
- WithTop.add_left_cancelproof · cited by 0