Theorems · Theorem · group theory
Matrix.smul_empty
∀ {α : Type u_1} {M : Type u_2} [inst : SMul M α] (x : M) (v : Fin 0 → α), x • v = ![]- Defined in
- Mathlib.Algebra.Group.Fin.Tuple
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Quot.sound
- Assumes
- SMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrix.vecEmptystatement · cited by 832
- Matrix.empty_eqproof · cited by 20
Cited by8
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.neg_of_Z_eq_zeroproof · cited by 3
- Height.mulHeight₁_div_eq_mulHeightproof · cited by 2
- Rat.mulHeight_self_one_eq_mulHeight_num_denproof · cited by 1
- Matrix.smul_vec3proof · cited by 1
- NumberField.mixedEmbedding.det_matrixToStdBasisproof · cited by 1
- ContDiffAt.harmonicAtproof · cited by 1
- NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mulproof · cited by 1
- Matrix.smul_vec2proof · cited by 0