Theorems · Theorem · group theory
mem_fixingAddSubgroup_iff
∀ (M : Type u_1) {α : Type u_2} [inst : AddGroup M] [inst_1 : AddAction M α] {s : Set α} {m : M},
m ∈ fixingAddSubgroup M s ↔ ∀ y ∈ s, m +ᵥ y = y- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- fixingAddSubgroupstatement and proof · cited by 50
Cited by9
Results whose statement or proof uses this declaration.
- mem_fixingAddSubgroup_iff_subset_fixedByproof · cited by 1
- Set.addConj_mem_fixingAddSubgroupproof · cited by 1
- SubAddAction.ofFixingAddSubgroup_of_singletonstatement · cited by 1
- AddAction.IsMultiplyPreprimitive.of_bijective_mapproof · cited by 1
- AddAction.fixingAddSubgroup_le_stabilizerproof · cited by 0
- SubAddAction.ofFixingAddSubgroup_of_singleton_bijectivestatement · cited by 0
- SubAddAction.mem_fixingAddSubgroup_insert_iffproof · cited by 0
- AddAction.isMultiplyPreprimitive_congrproof · cited by 0
- SubAddAction.fixingAddSubgroup_of_insertproof · cited by 0