Theorems · Theorem · group theory
smul_smul
∀ {M : Type u_1} {α : Type u_5} [inst : Monoid M] [inst_1 : MulAction M α] (a₁ a₂ : M) (b : α),
a₁ • a₂ • b = (a₁ * a₂) • b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 360 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 34 definitions · uses no axioms
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.
- Monoidstatement and proof · cited by 3,887
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
Cited by360
Results whose statement or proof uses this declaration.
- inv_smul_smulproof · cited by 76
- Submodule.mem_span_singletonproof · cited by 61
- smul_inv_smulproof · cited by 53
- Derivation.leibniz_powproof · cited by 10
- realPart_add_I_smul_imaginaryPartproof · cited by 10
- CategoryTheory.Functor.homologySequence_exact₂proof · cited by 8
- LieAlgebra.IsKilling.coe_corootSpace_eq_span_singletonproof · cited by 7
- Collinear.mem_affineSpan_of_mem_of_neproof · cited by 7
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- MeasureTheory.Measure.addHaarScalarFactor_eq_mulproof · cited by 6
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- midpoint_eq_smul_addproof · cited by 6
Showing the 200 most cited of 360.