Theorems · Theorem · group theory
add_nsmul
∀ {M : Type u_2} [inst : AddMonoid M] (a : M) (m n : ℕ), (m + n) • a = m • a + n • a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 44 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.
Cites1
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
Cited by45
Results whose statement or proof uses this declaration.
- Function.Periodic.nsmulproof · cited by 9
- mod_addOrderOf_nsmulproof · cited by 7
- AddCommGroup.ModEq.transproof · cited by 5
- multiplesHomproof · cited by 5
- Polynomial.smeval_natCastproof · cited by 4
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
- AddCommGroup.ModEq.add_iff_leftproof · cited by 3
- AddRightCancelMonoid.nsmul_eq_nsmul_iff_modEqproof · cited by 3
- AddAction.nsmul_mod_period_vaddproof · cited by 3
- AddCommGroup.ModEq.addproof · cited by 3
- AddOreLocalization.oreSub_zero_surjective_of_finite_leftproof · cited by 2
- AddOreLocalization.oreSub_zero_surjective_of_finite_rightproof · cited by 2