Theorems · Theorem · group theory
MulDistribMulAction.smul_one
∀ {M : Type u_9} {N : Type u_10} {inst : Monoid M} {inst_1 : Monoid N} [self : MulDistribMulAction M N] (r : M),
r • 1 = 1Multiplying 1 by a scalar gives 1
- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulDistribMulAction
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.
- Monoidstatement and proof · cited by 3,887
- MulDistribMulActionstatement and proof · cited by 120
Cited by9
Results whose statement or proof uses this declaration.
- MulDistribMulAction.toMonoidHomproof · cited by 10
- smul_algebraMapproof · cited by 7
- smul_inv₀'proof · cited by 2
- algebraMap.coe_smul'proof · cited by 2
- FixedPoints.submonoidproof · cited by 2
- SkewPolynomial.X_pow_eq_monomialproof · cited by 2
- SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_ofproof · cited by 0
- SkewMonoidAlgebra.single_eq_algebraMap_mul_ofproof · cited by 0
- SkewPolynomial.monomial_one_right_eq_X_powproof · cited by 0