Theorems · Theorem · group theory
AddAction.set_mem_fixedBy_iff
∀ {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 ∈ sIf a set s : Set α is in fixedBy (Set α) g, then all points of s will stay
in s after being moved by g.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.ext_iffproof · cited by 90
- Set.addActionSetstatement · cited by 39
- AddAction.fixedBystatement · cited by 26
- AddAction.mem_fixedByproof · cited by 12
- eq_neg_vadd_iffproof · cited by 9
- Set.mem_neg_vadd_set_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.vadd_mem_of_set_mem_fixedByproof · cited by 1