Theorems · Theorem · group theory
MulAction.coe_quotient_smul
∀ {G : Type u} {X : Type v} [inst : Group G] {H : Subgroup G} [inst_1 : H.Normal] [inst_2 : SMul G X]
[inst_3 : MulAction (G ⧸ H) X] [IsScalarTower G (G ⧸ H) X] (g : G) (x : X), ↑g • x = g • x- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- IsScalarTowerstatement and proof · cited by 3,896
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MulActionstatement and proof · cited by 1,294
- smul_eq_mulproof · cited by 357
- Subgroup.Normalstatement and proof · cited by 334
- QuotientGroup.mkstatement and proof · cited by 196
- smul_one_smulproof · cited by 43
- QuotientGroup.mk_oneproof · cited by 4
- MulAction.Quotient.smul_coeproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsGaloisGroup.quotientproof · cited by 1
- IsGaloisGroup.smulCommClassQuotientproof · cited by 1
- IsGaloisGroup.map_quotientMk'proof · cited by 1