Theorems · Theorem · group theory
neg_add_cancel_comm
∀ {G : Type u_1} [inst : AddCommGroup G] (a b : G), -a + b + a = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- add_commproof · cited by 1,535
- add_neg_cancel_leftproof · cited by 76
Cited by17
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.T_add_twoproof · cited by 20
- Polynomial.Chebyshev.U_add_twoproof · cited by 16
- Polynomial.Chebyshev.C_add_twoproof · cited by 13
- Polynomial.Chebyshev.S_add_twoproof · cited by 11
- Complex.Gamma_neg_nat_eq_zeroproof · cited by 4
- controlled_sum_of_mem_closureproof · cited by 2
- log_deriv_riemannZeta_add_inv_sub_sub_isBigOproof · cited by 1
- log_riemannZeta_add_log_sub_isBigO_ofRealproof · cited by 1
- ProbabilityTheory.lintegral_paretoPDF_eq_oneproof · cited by 1
- PointedCone.IsFaceOf.linealproof · cited by 0
- deriv_riemannZeta_add_inv_sub_sq_boundedproof · cited by 0
- Finset.prod_Ico_int_divproof · cited by 0