Theorems · Theorem · group theory
left_eq_add
∀ {M : Type u_4} [inst : AddMonoid M] [IsLeftCancelAdd M] {a b : M}, a = a + b ↔ b = 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 15 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.
Cites3
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
- IsLeftCancelAddstatement and proof · cited by 72
- add_eq_leftproof · cited by 37
Cited by15
Results whose statement or proof uses this declaration.
- Set.eq_univ_iff_ncardproof · cited by 4
- RootPairing.Base.root_sub_root_mem_of_mem_of_memproof · cited by 3
- Set.ncard_union_eq_iffproof · cited by 2
- Polynomial.eq_of_dvd_of_natDegree_le_of_leadingCoeffproof · cited by 1
- Int.ceil_eq_floor_add_one_iff_notMemproof · cited by 1
- MvPolynomial.eq_divMonomial_singleproof · cited by 1
- RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2proof · cited by 1
- IsOpen.eqOn_of_fderiv_eqproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducible_auxproof · cited by 1
- AddSubmonoid.closure_addIrreducibleproof · cited by 0
- Real.cos_eq_zero_iff_sin_eqproof · cited by 0
- Complex.cos_eq_zero_iff_sin_eqproof · cited by 0