English
Under IsPretransitive, for any a and x: Fin n.succ → α there exist g and y with g • x = ofStabilizer.snoc y.
Русский
При IsPretransitive, для любого a и x: Fin n.succ → α существуют g и y такие, что g • x = ofStabilizer.snoc y.
LaTeX
$$$\\exists g:\\,G\\;\\exists y:\\,Fin\\,n \\hookrightarrow \\mathrm{ofStabilizer}(G,a),\\ g \\cdot x = \\mathrm{ofStabilizer.snoc}(y).$$$
Lean4
instance : One (SubMulAction R M) where
one :=
{ carrier := Set.range fun r : R => r • (1 : M)
smul_mem' := fun r _ ⟨r', hr'⟩ => hr' ▸ ⟨r * r', mul_smul _ _ _⟩ }