[Merged by Bors] - perf(NormedSpace/OperatorNorm): fix simp call and clean up porting notes

Mathlib/Analysis/NormedSpace/OperatorNorm.lean

@@ -394,11 +394,6 @@ theorem op_norm_comp_le (f : E →SL[σ₁₂] F) : ‖h.comp f‖ ≤ ‖h‖ *
       exact h.le_op_norm_of_le (f.le_op_norm x)⟩
 #align continuous_linear_map.op_norm_comp_le ContinuousLinearMap.op_norm_comp_le
 
--- Porting note: restatement of `op_norm_comp_le` for linear maps.
-/-- The operator norm is submultiplicative. -/
-theorem op_norm_comp_le' (h : Eₗ →L[𝕜] Fₗ) (f : E →L[𝕜] Eₗ) : ‖h.comp f‖ ≤ ‖h‖ * ‖f‖ :=
-  op_norm_comp_le h f
-
 theorem op_nnnorm_comp_le [RingHomIsometric σ₁₃] (f : E →SL[σ₁₂] F) : ‖h.comp f‖₊ ≤ ‖h‖₊ * ‖f‖₊ :=
   op_norm_comp_le h f
 #align continuous_linear_map.op_nnnorm_comp_le ContinuousLinearMap.op_nnnorm_comp_le
@@ -409,12 +404,10 @@ instance toSemiNormedRing : SeminormedRing (E →L[𝕜] E) :=
     norm_mul := fun f g => op_norm_comp_le f g }
 #align continuous_linear_map.to_semi_normed_ring ContinuousLinearMap.toSemiNormedRing
 
--- Porting FIXME: replacing `(algebra : Algebra 𝕜 (E →L[𝕜] E))` with
--- just `algebra` below causes a massive timeout.
 /-- For a normed space `E`, continuous linear endomorphisms form a normed algebra with
 respect to the operator norm. -/
 instance toNormedAlgebra : NormedAlgebra 𝕜 (E →L[𝕜] E) :=
-  { (algebra : Algebra 𝕜 (E →L[𝕜] E)) with
+  { algebra with
     norm_smul_le := by
       intro c f
       apply op_norm_smul_le c f}
@@ -682,12 +675,10 @@ def mkContinuousOfExistsBound₂ (f : E →ₛₗ[σ₁₃] F →ₛₗ[σ₂₃
     { toFun := fun x => (f x).mkContinuousOfExistsBound <| let ⟨C, hC⟩ := h; ⟨C * ‖x‖, hC x⟩
       map_add' := fun x y => by
         ext z
-        rw [ContinuousLinearMap.add_apply, mkContinuousOfExistsBound_apply,
-          mkContinuousOfExistsBound_apply, mkContinuousOfExistsBound_apply, map_add, add_apply]
+        simp
       map_smul' := fun c x => by
         ext z
-        rw [ContinuousLinearMap.smul_apply, mkContinuousOfExistsBound_apply,
-          mkContinuousOfExistsBound_apply, map_smulₛₗ, smul_apply] } <|
+        simp } <|
     let ⟨C, hC⟩ := h; ⟨max C 0, norm_mkContinuous₂_aux f C hC⟩
 
 /-- Create a bilinear map (represented as a map `E →L[𝕜] F →L[𝕜] G`) from the corresponding linear
@@ -734,10 +725,8 @@ def flip (f : E →SL[σ₁₃] F →SL[σ₂₃] G) : F →SL[σ₂₃] E →SL
     ‖f‖ fun y x => (f.le_op_norm₂ x y).trans_eq <| by simp only [mul_right_comm]
 #align continuous_linear_map.flip ContinuousLinearMap.flip
 
--- Porting note: in mathlib3, in the proof `norm_nonneg (flip f)` was just `norm_nonneg _`,
--- but this causes a defeq error now.
 private theorem le_norm_flip (f : E →SL[σ₁₃] F →SL[σ₂₃] G) : ‖f‖ ≤ ‖flip f‖ :=
-  f.op_norm_le_bound₂ (norm_nonneg (flip f)) fun x y => by
+  f.op_norm_le_bound₂ (norm_nonneg _) fun x y => by
     rw [mul_right_comm]
     exact (flip f).le_op_norm₂ y x
 
@@ -960,7 +949,6 @@ variable (M₁ : Type u₁) [SeminormedAddCommGroup M₁] [NormedSpace 𝕜 M₁
 
 variable {Eₗ} (𝕜)
 
-set_option maxHeartbeats 400000 in
 /-- `ContinuousLinearMap.prodMap` as a continuous linear map. -/
 def prodMapL : (M₁ →L[𝕜] M₂) × (M₃ →L[𝕜] M₄) →L[𝕜] M₁ × M₃ →L[𝕜] M₂ × M₄ :=
   ContinuousLinearMap.copy
@@ -981,22 +969,8 @@ def prodMapL : (M₁ →L[𝕜] M₂) × (M₃ →L[𝕜] M₄) →L[𝕜] M₁
       apply funext
       rintro ⟨φ, ψ⟩
       refine' ContinuousLinearMap.ext fun ⟨x₁, x₂⟩ => _
-      -- Porting note: mathport suggested:
-      -- ```
-      -- simp only [add_apply, coe_comp', coe_fst', Function.comp_apply, compL_apply, flip_apply,
-      --   coe_snd', inl_apply, inr_apply, Prod.mk_add_mk, add_zero, zero_add, coe_prodMap'
-      --   Prod_map, Prod.mk.inj_iff, eq_self_iff_true, and_self_iff]
-      -- rfl
-      -- ```
-      -- Frustratingly, in `mathlib3` we can use:
-      -- ```
-      -- dsimp   -- ⊢ (⇑φ x.fst, ⇑ψ x.snd) = (⇑φ x.fst + 0, 0 + ⇑ψ x.snd)
-      -- simp
-      -- ```
-      -- Here neither `dsimp` or `simp` seem to make progress.
-      repeat first | rw [add_apply] | rw [comp_apply] | rw [flip_apply] | rw [compL_apply]
-      simp only [coe_prodMap', Prod_map, coe_fst', inl_apply, coe_snd', inr_apply, Prod.mk_add_mk,
-        add_zero, zero_add])
+      dsimp
+      simp)
 #align continuous_linear_map.prod_mapL ContinuousLinearMap.prodMapL
 
 variable {M₁ M₂ M₃ M₄}

Mathlib/Topology/MetricSpace/PseudoMetric.lean

@@ -1274,7 +1274,8 @@ theorem PseudoMetricSpace.replaceTopology_eq {γ} [U : TopologicalSpace γ] (m :
 is everywhere finite, by pushing the edistance to reals. We set it up so that the edist and the
 uniformity are defeq in the pseudometric space and the pseudoemetric space. In this definition, the
 distance is given separately, to be able to prescribe some expression which is not defeq to the
-push-forward of the edistance to reals. -/
+push-forward of the edistance to reals. See note [reducible non-instances]. -/
+@[reducible]
 def PseudoEMetricSpace.toPseudoMetricSpaceOfDist {α : Type u} [e : PseudoEMetricSpace α]
     (dist : α → α → ℝ) (edist_ne_top : ∀ x y : α, edist x y ≠ ⊤)
     (h : ∀ x y, dist x y = ENNReal.toReal (edist x y)) : PseudoMetricSpace α where