Theorems · Theorem · group theory
AddAction.mem_fixedBy
∀ {M : Type u_1} {α : Type u_3} [inst : AddMonoid M] [inst_1 : AddAction M α] {m : M} {a : α},
a ∈ AddAction.fixedBy α m ↔ m +ᵥ a = a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.fixedBystatement · cited by 26
Cited by12
Results whose statement or proof uses this declaration.
- AddAction.fixedBy_negproof · cited by 3
- AddAction.movedBy_mem_fixedBy_of_addCommuteproof · cited by 2
- AddAction.mem_fixedBy_zsmulproof · cited by 2
- AddAction.vadd_mem_fixedBy_iff_mem_fixedByproof · cited by 2
- AddAction.fixedBy_mem_fixedBy_of_addCommuteproof · cited by 2
- mem_fixingAddSubgroup_iff_subset_fixedByproof · cited by 1
- AddAction.set_mem_fixedBy_iffproof · cited by 1
- AddAction.fixedBy_eq_univ_iff_eq_zeroproof · cited by 1
- AddAction.mem_fixedBy_zmultiples_iff_mem_fixedByproof · cited by 0
- AddAction.vadd_fixedByproof · cited by 0
- AddAction.fixedBy_addproof · cited by 0
- AddActionHom.map_mem_fixedByproof · cited by 0