Theorems · Theorem · group theory
add_eq_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
- 37 results in Mathlib
- Foundations
- Depth 8 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
- add_zeroproof · cited by 2,707
- IsLeftCancelAddstatement and proof · cited by 72
- add_left_cancel_iffproof · cited by 17
Cited by37
Results whose statement or proof uses this declaration.
- left_eq_addproof · cited by 15
- sub_eq_selfproof · cited by 11
- norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zeroproof · cited by 5
- norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zeroproof · cited by 5
- norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zeroproof · cited by 3
- Lagrange.sum_basisproof · cited by 3
- bind₁_wittPolynomial_xInTermsOfWproof · cited by 3
- AddCommGroup.tfae_modEqproof · cited by 3
- one_add_mul_self_lt_rpow_one_addproof · cited by 2
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_ltproof · cited by 2
- ZMod.orderOf_one_add_mul_prime_powproof · cited by 2