Theorems · Theorem · group theory
Subgroup.smul_leftQuotientEquiv
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {F : Type u_2} [inst_1 : Group F] [inst_2 : MulAction F G]
[inst_3 : MulAction.QuotientAction F H] (f : F) (S : H.LeftTransversal) (q : G ⧸ H),
f • ↑(⋯.leftQuotientEquiv q) = ↑(⋯.leftQuotientEquiv (f • q))- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MulActionstatement and proof · cited by 1,294
- Subgroup.IsComplementstatement · cited by 94
- Quotient.inductionOn'proof · cited by 69
- Subgroup.IsComplement.leftQuotientEquivstatement · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.smul_apply_eq_smul_apply_inv_smulproof · cited by 4