instDistribMulActionAut — Mathlib

English

The automorphism group Aut P naturally acts on M as a distributive-multiplicative action, i.e., Aut P forms a DistribMulAction on M via weightHom.

Русский

Группа автоморфизмов Aut P естественно действует на M как распределённо-мультипликативное действие, через weightHom.

LaTeX

$$$\\\\text{Aut}(P) \\\\curvearrowright M \\\\text{ via weightHom } P.$$$

Lean4

instance : DistribMulAction P.Aut M where
  smul w x := weightHom P w x
  one_smul _ := rfl
  mul_smul _ _ _ := rfl
  smul_zero w := show weightHom P w 0 = 0 by simp
  smul_add w x y := show weightHom P w (x + y) = weightHom P w x + weightHom P w y by simp

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