Theorems · Theorem · group theory
AddLeftCancelMonoid.add_ne_zero
∀ {α : Type u} [inst : AddLeftCancelMonoid α] [Subsingleton (AddUnits α)] {a b : α}, a + b ≠ 0 ↔ a ≠ 0 ∨ b ≠ 0- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddUnitsstatement and proof · cited by 325
- AddLeftCancelMonoidstatement and proof · cited by 37
- not_iff_commproof · cited by 32
- AddLeftCancelMonoid.add_eq_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- add_ne_zero'proof · cited by 0