Theorems · Theorem · group theory
two_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (a : G), 2 • a = a + a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SubNegMonoid
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.
- SubNegMonoidstatement and proof · cited by 79
- two_nsmulproof · cited by 67
- ofNat_zsmulproof · cited by 24
Cited by21
Results whose statement or proof uses this declaration.
- Orientation.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eqproof · cited by 3
- Module.eq_of_mapsTo_reflection_of_memproof · cited by 2
- Real.Angle.two_zsmul_eq_pi_iffproof · cited by 2
- Function.Antiperiodic.even_zsmul_periodicproof · cited by 2
- Real.Angle.two_zsmul_eq_iff_eq_of_abs_toReal_lt_pi_div_twoproof · cited by 2
- Real.Angle.two_zsmul_eq_zero_iffproof · cited by 1
- Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_piproof · cited by 1
- Real.Angle.tan_eq_of_two_zsmul_eqproof · cited by 1
- Real.Angle.abs_cos_eq_abs_sin_of_two_zsmul_add_two_zsmul_eq_piproof · cited by 1
- Real.Angle.abs_sin_eq_of_two_zsmul_eqproof · cited by 1
- Real.Angle.sign_two_zsmul_eq_sign_iffproof · cited by 1
- Summable.tendsto_zero_of_even_summable_symmetricIccproof · cited by 1