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Theorems · Theorem · group theory

AddAction.vadd_orbit_subset

∀ {M : Type u_1} {α : Type u_3} [inst : AddMonoid M] [inst_1 : AddAction M α] (m : M) (a : α),
  m +ᵥ AddAction.orbit M a ⊆ AddAction.orbit M a
Defined in
Mathlib.GroupTheory.GroupAction.Defs
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidAddAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddAction.vadd_orbit · cited by 3AddAction.vadd_orbitvadd_closure_orbit_subset · cited by 1vadd_closure_orbit_subsetSet · cited by 53352SetAddMonoid · cited by 2864AddMonoidHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionSet.vaddSet · cited by 403Set.vaddSetAddAction.orbit · cited by 86AddAction.orbitSet.MapsTo.image_subset · cited by 49MapsTo.image_subsetAddAction.mapsTo_vadd_orbit · cited by 2AddAction.mapsTo_vadd_orb…AddAction.vadd_orbit_subsetCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.