Theorems · Theorem · group theory
AddLeftCancelMonoid.eq_zero_of_add_right
∀ {α : Type u} [inst : AddLeftCancelMonoid α] [Subsingleton (AddUnits α)] {a b : α}, a + b = 0 → a = 0- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
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.
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- AddUnitsstatement and proof · cited by 325
- AddLeftCancelMonoidstatement and proof · cited by 37
- add_left_cancel_iffproof · cited by 17
- AddUnits.negproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- AddLeftCancelMonoid.add_eq_zeroproof · cited by 4
- AddLeftCancelMonoid.eq_zero_of_add_leftproof · cited by 2
- eq_zero_of_add_right'proof · cited by 0