@@ -273,14 +273,6 @@ def compSL : (F βSL[Οββ] G) βL[πβ] (E βSL[Οββ] F) βSL[Ο
273273 Pi.smul_apply])
274274 1 fun f g => by simpa only [one_mul] using opNorm_comp_le f g
275275
276- #adaptation_note
277- /--
278- Before https://github.com/leanprover/lean4/pull/4119 we had to create a local instance:
279- ```
280- letI : Norm ((F βSL[Οββ] G) βL[πβ] (E βSL[Οββ] F) βSL[Οββ] E βSL[Οββ] G) :=
281- hasOpNorm (πβ := πβ) (E := F βSL[Οββ] G) (F := (E βSL[Οββ] F) βSL[Οββ] E βSL[Οββ] G)
282- ```
283- -/
284276set_option maxSynthPendingDepth 2 in
285277theorem norm_compSL_le : βcompSL E F G Οββ Οβββ β€ 1 :=
286278 LinearMap.mkContinuousβ_norm_le _ zero_le_one _
@@ -309,14 +301,6 @@ variable (π Οββ Οββ E Fβ Gβ)
309301def compL : (Fβ βL[π] Gβ) βL[π] (E βL[π] Fβ) βL[π] E βL[π] Gβ :=
310302 compSL E Fβ Gβ (RingHom.id π) (RingHom.id π)
311303
312- #adaptation_note
313- /--
314- Before https://github.com/leanprover/lean4/pull/4119 we had to create a local instance:
315- ```
316- letI : Norm ((Fβ βL[π] Gβ) βL[π] (E βL[π] Fβ) βL[π] E βL[π] Gβ) :=
317- hasOpNorm (πβ := π) (E := Fβ βL[π] Gβ) (F := (E βL[π] Fβ) βL[π] E βL[π] Gβ)
318- ```
319- -/
320304set_option maxSynthPendingDepth 2 in
321305theorem norm_compL_le : βcompL π E Fβ Gββ β€ 1 :=
322306 norm_compSL_le _ _ _ _ _
@@ -339,31 +323,13 @@ def precompL (L : E βL[π] Fβ βL[π] Gβ) : (Eβ βL[π] E) βL[
339323@[simp] lemma precompL_apply (L : E βL[π] Fβ βL[π] Gβ) (u : Eβ βL[π] E) (f : Fβ) (g : Eβ) :
340324 precompL Eβ L u f g = L (u g) f := rfl
341325
342- #adaptation_note
343- /--
344- Before https://github.com/leanprover/lean4/pull/4119
345- we had to create a local instance in the signature:
346- ```
347- letI : SeminormedAddCommGroup ((Eβ βL[π] Fβ) βL[π] Eβ βL[π] Gβ) := inferInstance
348- letI : NormedSpace π ((Eβ βL[π] Fβ) βL[π] Eβ βL[π] Gβ) := inferInstance
349- ```
350- -/
351326set_option maxSynthPendingDepth 2 in
352327theorem norm_precompR_le (L : E βL[π] Fβ βL[π] Gβ) : βprecompR Eβ Lβ β€ βLβ :=
353328 calc
354329 βprecompR Eβ Lβ β€ βcompL π Eβ Fβ Gββ * βLβ := opNorm_comp_le _ _
355330 _ β€ 1 * βLβ := mul_le_mul_of_nonneg_right (norm_compL_le _ _ _ _) (norm_nonneg L)
356331 _ = βLβ := by rw [one_mul]
357332
358- #adaptation_note
359- /--
360- Before https://github.com/leanprover/lean4/pull/4119
361- we had to create a local instance in the signature:
362- ```
363- letI : Norm ((Eβ βL[π] E) βL[π] Fβ βL[π] Eβ βL[π] Gβ) :=
364- hasOpNorm (πβ := π) (E := Eβ βL[π] E) (F := Fβ βL[π] Eβ βL[π] Gβ)
365- ```
366- -/
367333set_option maxSynthPendingDepth 2 in
368334theorem norm_precompL_le (L : E βL[π] Fβ βL[π] Gβ) : βprecompL Eβ Lβ β€ βLβ := by
369335 rw [precompL, opNorm_flip, β opNorm_flip L]
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