Theorems · Theorem · group theory

Subgroup.smul_toLeftFun

∀ {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) (g : G),
  f • ↑(⋯.toLeftFun g) = ↑(⋯.toLeftFun (f • g))

Defined in: Mathlib.GroupTheory.Complement
Cited by: 1 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group Group MulAction MulAction.QuotientAction

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
SetLike.coestatement · cited by 8,199
Groupstatement and proof · cited by 6,238
Subgroupstatement and proof · cited by 3,593
MulActionstatement and proof · cited by 1,294
Subgroup.IsComplementstatement · cited by 94
ExistsUnique.uniqueproof · cited by 42
Subgroup.LeftTransversalstatement and proof · cited by 13
MulAction.QuotientActionstatement and proof · cited by 8
Subgroup.IsComplement.toLeftFunstatement · cited by 4
Subgroup.IsComplement.inv_toLeftFun_mul_memproof · cited by 3
Subgroup.isComplement_iff_existsUnique_inv_mul_memproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Subgroup.smul_leftQuotientEquivproof · cited by 1