Theorems · Theorem · group theory
mem_fixingSubgroup_compl_iff_movedBy_subset
∀ (M : Type u_1) {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] {s : Set α} {m : M},
m ∈ fixingSubgroup M sᶜ ↔ (MulAction.fixedBy α m)ᶜ ⊆ s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, 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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Compl.complstatement and proof · cited by 2,925
- MulActionstatement and proof · cited by 1,294
- fixingSubgroupstatement · cited by 83
- MulAction.fixedBystatement and proof · cited by 36
- Set.compl_subset_commproof · cited by 23
- mem_fixingSubgroup_iff_subset_fixedByproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- orbit_fixingSubgroup_compl_subsetproof · cited by 0