Theorems · Theorem · group theory
nsmul_sub
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b : α) (n : ℕ), n • (a - b) = n • a - n • b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- sub_eq_add_negproof · cited by 1,023
- SubtractionCommMonoidstatement and proof · cited by 79
- neg_nsmulproof · cited by 19
- nsmul_addproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- isAddTorsionFree_iff_not_isOfFinAddOrderproof · cited by 4
- Real.Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_piproof · cited by 1