Theorems · Theorem · group theory
mem_fixingAddSubgroup_iff_subset_fixedBy
∀ (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 ↔ s ⊆ AddAction.fixedBy α m- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- fixingAddSubgroupstatement · cited by 50
- AddAction.fixedBystatement and proof · cited by 26
- AddAction.mem_fixedByproof · cited by 12
- mem_fixingAddSubgroup_iffproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- mem_fixingAddSubgroup_compl_iff_movedBy_subsetproof · cited by 1