Theorems · Theorem · group theory
AddAction.mapsTo_vadd_orbit
∀ {M : Type u_1} {α : Type u_3} [inst : AddMonoid M] [inst_1 : AddAction M α] (m : M) (a : α),
Set.MapsTo (fun x => m +ᵥ x) (AddAction.orbit M a) (AddAction.orbit M a)- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.MapsTostatement · cited by 732
- Set.range_subset_iffproof · cited by 99
- AddAction.orbitstatement · cited by 86
- AddSemigroupAction.add_vaddproof · cited by 43
- Set.mapsTo_iff_subset_preimageproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.vadd_orbit_subsetproof · cited by 2
- AddAction.orbitRel.Quotient.mapsTo_vadd_orbitproof · cited by 0