instModuleCarrierMkOfSMul' — Mathlib

English

mkOfSMul' φ is equipped with an R-module structure on its carrier, i.e. all module axioms hold with action r·x = φ(r)(x).

Русский

mkOfSMul' φ на носителе имеет структуру модуля над R; акção r·x задаётся как φ(r)(x).

LaTeX

$$$\text{Module }R\; (\mathrm{mkOfSMul}'\phi).\text{carrier}$ with $r\cdot x = \phi(r)(x)$.$$

Lean4

instance : Module R (mkOfSMul' φ) where
  smul_zero _ := map_zero (N := A) _
  smul_add _ _ _ := map_add (N := A) _ _ _
  one_smul := by simp
  mul_smul := by simp
  add_smul _ _ _ := by simp; rfl
  zero_smul := by simp

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