Theorems · Theorem · group theory
MulAction.Quotient.smul_coe
∀ {G : Type u} {X : Type v} [inst : Group G] [inst_1 : Monoid X] [inst_2 : MulAction X G] (H : Subgroup G)
[inst_3 : MulAction.QuotientAction X H] (b : X) (g : G), b • ↑g = ↑(b • g)- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- MulActionstatement and proof · cited by 1,294
- QuotientGroup.mkstatement · cited by 196
- MulAction.QuotientActionstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.coe_quotient_smulproof · cited by 3