Theorems · Theorem · group theory
add_neg_cancel_comm_assoc
∀ {G : Type u_1} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 8 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
- neg_add_cancel_rightproof · cited by 75
Cited by16
Results whose statement or proof uses this declaration.
- add_sub_add_left_eq_subproof · cited by 20
- sub_sub_selfproof · cited by 12
- Real.arccos_cosproof · cited by 4
- zero_mem_tangentConeAtproof · cited by 2
- Int.fib_add_twoproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_dist_sq_eqproof · cited by 1
- two_nsmul_inf_eq_add_sub_abs_subproof · cited by 1
- Submodule.mem_span_insert'proof · cited by 1
- tendsto_integral_comp_smul_smul_of_integrable'proof · cited by 1
- integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1proof · cited by 1
- Asymptotics.superpolynomialDecay_iff_isBigOproof · cited by 1
- MeasureTheory.lconvolution_commproof · cited by 0