Theorems · Theorem · group theory
add_ne_left
∀ {M : Type u_4} [inst : AddMonoid M] [IsLeftCancelAdd M] {a b : M}, a + b ≠ a ↔ b ≠ 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddMonoidIsLeftCancelAdd
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.
- AddMonoidstatement and proof · cited by 2,864
- Iff.notproof · cited by 489
- IsLeftCancelAddstatement and proof · cited by 72
- add_eq_leftproof · cited by 37
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.LFunction_ne_zero_of_re_eq_oneproof · cited by 1