instOne — Mathlib

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 _ _ _⟩ }

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