cusps_subMulAction — Mathlib

English

The cusps form a subgroup-acting set under 𝒢 with the action given by IsCusp.smul_of_mem.

Русский

С cusp-ы образуют множество, на котором действует 𝒢, через действие, задаваемое IsCusp.smul_of_mem.

LaTeX

$$$\\text{cusps\_subMulAction}(\\mathcal{G}) = \\text{SubMulAction } \\mathcal{G} (\\mathrm{OnePoint}(\\mathbb{R}) )$ with carrier $\\{c : \\mathrm{OnePoint}(\\mathbb{R}) \\mid IsCusp(c, \\mathcal{G})\\}$ and $g \\cdot c$ preserves cusp by $IsCusp.smul\_of\_mem$.$$

Lean4

/-- The action of `𝒢` on its own cusps. -/
def cusps_subMulAction (𝒢 : Subgroup (GL (Fin 2) ℝ)) : SubMulAction 𝒢 (OnePoint ℝ)
    where
  carrier := {c | IsCusp c 𝒢}
  smul_mem' g _ hc := IsCusp.smul_of_mem hc g.property

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