Theorems · Theorem · group theory

SubAddAction.fixingAddSubgroup_map_addConj_eq

∀ {M : Type u_1} {α : Type u_2} [inst : AddGroup M] [inst_1 : AddAction M α] {s t : Set α} {g : M},
  g +ᵥ t = s →
    AddSubgroup.map (AddEquiv.toAddMonoidHom (AddAut.addConj g)) (fixingAddSubgroup M t) = fixingAddSubgroup M s

Defined in: Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
Cited by: 1 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Quot.sound
Assumes: AddGroup AddAction

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Cites28

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

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement · cited by 3,232
AddMonoidHomstatement · cited by 3,230
add_zeroproof · cited by 2,707
zero_addproof · cited by 2,366
HVAdd.hVAddstatement and proof · cited by 1,820
neg_negproof · cited by 960
AddActionstatement and proof · cited by 820
add_assocproof · cited by 746
Set.vaddSetstatement · cited by 403

Cited by2

Results whose statement or proof uses this declaration.

SubAddAction.fixingAddSubgroupEquivFixingAddSubgroupproof · cited by 4
SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_addConjproof · cited by 0