Theorems · Theorem · group theory
add_eq_right
∀ {M : Type u_4} [inst : AddMonoid M] [IsRightCancelAdd M] {a b : M}, a + b = b ↔ a = 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddMonoidIsRightCancelAdd
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
- zero_addproof · cited by 2,366
- IsRightCancelAddstatement and proof · cited by 69
- add_right_cancel_iffproof · cited by 19
Cited by17
Results whose statement or proof uses this declaration.
- right_eq_addproof · cited by 13
- IsCyclotomicExtension.discr_prime_powproof · cited by 3
- UniqueFactorizationMonoid.card_factors_of_irreducibleproof · cited by 2
- QuotientAddGroup.norm_mkproof · cited by 2
- sub_eq_neg_selfproof · cited by 2
- Affine.Simplex.closedInterior_eq_interior_unionproof · cited by 1
- PartitionOfUnity.sum_finsupport'proof · cited by 1
- Affine.Simplex.closedInterior_inter_shift_zeroproof · cited by 1
- add_notMem_of_addOrderOf_eq_twoproof · cited by 1
- Orientation.abs_oangle_sub_left_toReal_lt_pi_div_twoproof · cited by 1
- RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2proof · cited by 1
- AddCircle.nsmul_eq_zero_iffproof · cited by 1