Theorems · Theorem · group theory
two_nsmul
∀ {M : Type u_2} [inst : AddMonoid M] (a : M), 2 • a = a + a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- succ_nsmulproof · cited by 65
- one_nsmulproof · cited by 63
Cited by67
Results whose statement or proof uses this declaration.
- abs_nonnegproof · cited by 168
- two_zsmulproof · cited by 21
- even_iff_exists_two_nsmulproof · cited by 6
- ArchimedeanClass.min_le_mk_addproof · cited by 5
- self_eq_negproof · cited by 5
- ArchimedeanClass.mk_add_eq_mk_leftproof · cited by 4
- Real.Angle.coe_pi_add_coe_piproof · cited by 3
- Function.Antiperiodic.periodicproof · cited by 3
- ConvexOn.isBoundedUnder_absproof · cited by 2
- AffineEquiv.injective_pointReflection_left_of_moduleproof · cited by 2
- Real.Angle.eq_neg_self_iffproof · cited by 2
- Function.Antiperiodic.even_zsmul_periodicproof · cited by 2