Theorems · Theorem · group theory
AddAction.vadd_mem_of_set_mem_fixedBy
∀ {α : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {s : Set α} {g : G},
s ∈ AddAction.fixedBy (Set α) g → ∀ {x : α}, g +ᵥ x ∈ s ↔ x ∈ s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.addActionSetstatement · cited by 39
- AddAction.fixedBystatement and proof · cited by 26
- AddAction.set_mem_fixedBy_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- orbit_fixingAddSubgroup_compl_subsetproof · cited by 0