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