nevanlinna/Nevanlinna/smulImprovement.lean

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import Mathlib.Analysis.Complex.CauchyIntegral
--import Mathlib.Analysis.Complex.Module
example simplificationTest₁
{E : Type*} [NormedAddCommGroup E] [NormedSpace E] [IsScalarTower E]
{v : E}
{z : } :
z • v = z.re • v + Complex.I • z.im • v := by
/-
An attempt to write "rw [add_smul]" will fail with "did not find instance of
the pattern in the target -- expression (?r + ?s) • ?x".
-/
sorry
theorem add_smul'
(𝕜₁ : Type*) [NontriviallyNormedField ]
{𝕜₂ : Type*} [NontriviallyNormedField ] [NormedAlgebra ]
{E : Type*} [NormedAddCommGroup E] [NormedSpace E] [CompleteSpace E] [IsScalarTower E]
{v : E}
{r s : } :
(r + s) • v = r • v + s • v :=
Module.add_smul r s v
theorem smul_add' (a : M) (b₁ b₂ : A) : a • (b₁ + b₂) = a • b₁ + a • b₂ :=
DistribSMul.smul_add _ _ _
#align smul_add smul_add
example simplificationTest₂
{v : E}
{z : } :
z • v = z.re • v + Complex.I • z.im • v := by
sorry