@@ -256,7 +256,7 @@ lemma interp_exp_inv_ne_zero (ht : t ∈ Ioo 0 1) (hp₀ : p₀ > 0)
256256lemma preservation_interpolation (ht : t ∈ Ioo 0 1 ) (hp₀ : p₀ > 0 )
257257 (hp₁ : p₁ > 0 ) (hp : p⁻¹ = (1 - ENNReal.ofReal t) * p₀⁻¹ + ENNReal.ofReal t * p₁⁻¹) :
258258 p⁻¹.toReal = (1 - t) * (p₀⁻¹).toReal + t * (p₁⁻¹).toReal := by
259- rw [← one_toReal , ← toReal_ofReal ht.1 .le, ← ENNReal.toReal_sub_of_le]
259+ rw [← toReal_one , ← toReal_ofReal ht.1 .le, ← ENNReal.toReal_sub_of_le]
260260 · rw [← toReal_mul, ← toReal_mul, ← toReal_add]
261261 · exact congrArg ENNReal.toReal hp
262262 · exact mul_ne_top (sub_ne_top (top_ne_one.symm)) (inv_ne_top.mpr hp₀.ne')
@@ -269,7 +269,7 @@ lemma preservation_positivity_inv_toReal (ht : t ∈ Ioo 0 1) (hp₀ : p₀ > 0)
269269 0 < (1 - t) * (p₀⁻¹).toReal + t * (p₁⁻¹).toReal := by
270270 rcases (eq_or_ne p₀ ⊤) with p₀eq_top | p₀ne_top
271271 · rw [p₀eq_top]
272- simp only [inv_top, zero_toReal , mul_zero, zero_add]
272+ simp only [inv_top, toReal_zero , mul_zero, zero_add]
273273 apply mul_pos ht.1
274274 rw [toReal_inv]
275275 refine inv_pos_of_pos (exp_toReal_pos hp₁ ?_)
@@ -521,7 +521,7 @@ lemma ζ_equality₇ (ht : t ∈ Ioo 0 1) (hp₀ : p₀ > 0) (hq₀ : q₀ > 0)
521521 ζ p₀ q₀ p₁ q₁ t = p₀.toReal / (p₀.toReal - p.toReal) := by
522522 rw [ζ_equality₁ ht, ← preservation_interpolation ht hp₀ hp₁ hp,
523523 ← preservation_interpolation ht hq₀ hq₁ hq, hq₀']
524- simp only [inv_top, zero_toReal , sub_zero, mul_zero, zero_add]
524+ simp only [inv_top, toReal_zero , sub_zero, mul_zero, zero_add]
525525 have obs : p₀.toReal * p.toReal * q.toReal > 0 :=
526526 mul_pos (mul_pos (toReal_pos hp₀.ne' hp₀') (interp_exp_toReal_pos ht hp₀ hp₁ hp₀p₁ hp))
527527 (interp_exp_toReal_pos ht hq₀ hq₁ hq₀q₁ hq)
@@ -564,7 +564,7 @@ lemma ζ_eq_top_top (ht : t ∈ Ioo 0 1) (hp₀ : p₀ > 0) (hq₀ : q₀ > 0)
564564 ζ p₀ q₀ p₁ q₁ t = 1 := by
565565 rw [ζ_equality₂ ht, ← preservation_interpolation ht hp₀ hp₁ hp,
566566 ← preservation_interpolation ht hq₀ hq₁ hq, hp₁', hq₁']
567- simp only [inv_top, zero_toReal , sub_zero]
567+ simp only [inv_top, toReal_zero , sub_zero]
568568 rw [mul_comm, div_eq_mul_inv, mul_inv_cancel₀]
569569 exact (mul_pos (interp_exp_inv_pos ht hq₀ hq₁ hq₀q₁ hq)
570570 (interp_exp_inv_pos ht hp₀ hp₁ hp₀p₁ hp)).ne'
@@ -1124,7 +1124,7 @@ lemma d_eq_top₀ (hp₀ : p₀ > 0) (hq₁ : q₁ > 0) (hp₀' : p₀ ≠ ⊤)
11241124 (↑C₀ ^ p₀.toReal * eLpNorm f p μ ^ p.toReal).toReal ^ p₀.toReal⁻¹ := by
11251125 unfold d
11261126 rw [hq₀']
1127- simp only [inv_top, zero_toReal , sub_zero, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
1127+ simp only [inv_top, toReal_zero , sub_zero, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
11281128 div_one]
11291129 rw [mul_div_cancel_right₀]
11301130 · rw [div_eq_mul_inv, mul_inv_cancel₀, ENNReal.rpow_one]
@@ -1141,7 +1141,7 @@ lemma d_eq_top₁ (hq₀ : q₀ > 0) (hp₁ : p₁ > 0) (hp₁' : p₁ ≠ ⊤)
11411141 (↑C₁ ^ p₁.toReal * eLpNorm f p μ ^ p.toReal).toReal ^ p₁.toReal⁻¹ := by
11421142 unfold d
11431143 rw [hq₁']
1144- simp only [inv_top, zero_toReal , zero_sub, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
1144+ simp only [inv_top, toReal_zero , zero_sub, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
11451145 one_div]
11461146 rw [div_neg, div_neg]
11471147 rw [mul_div_cancel_right₀]
@@ -1172,7 +1172,7 @@ lemma d_eq_top_top (hq₀ : q₀ > 0) (hq₀q₁ : q₀ ≠ q₁) (hp₁' : p₁
11721172 @d α E₁ m p p₀ q₀ p₁ q₁ C₀ C₁ μ _ f = C₁ := by
11731173 unfold d
11741174 rw [hp₁', hq₁']
1175- simp only [inv_top, zero_toReal , zero_sub, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
1175+ simp only [inv_top, toReal_zero , zero_sub, zero_div, ENNReal.rpow_zero, mul_zero, mul_one,
11761176 zero_mul, one_div]
11771177 rw [div_neg, div_eq_mul_inv, mul_inv_cancel₀]
11781178 · rw [ENNReal.rpow_neg, ENNReal.rpow_one, inv_inv, coe_toReal]
@@ -2894,7 +2894,7 @@ lemma weaktype_estimate_trunc_compl_top {C₀ : ℝ≥0} (hC₀ : C₀ > 0) {p p
28942894 have term_ne_top : (ENNReal.ofNNReal C₀) ^ p₀.toReal * eLpNorm f p μ ^ p.toReal ≠ ⊤
28952895 := mul_ne_top (rpow_ne_top' (ENNReal.coe_ne_zero.mpr hC₀.ne') coe_ne_top)
28962896 (rpow_ne_top' snorm_p_pos (MemLp.eLpNorm_ne_top hf))
2897- have d_pos : d > 0 := hdeq ▸ Real.rpow_pos_of_pos (zero_toReal ▸
2897+ have d_pos : d > 0 := hdeq ▸ Real.rpow_pos_of_pos (toReal_zero ▸
28982898 toReal_strict_mono term_ne_top term_pos) _
28992899 have a_pos : a > 0 := by rw [ha]; positivity
29002900 have obs : MemLp (f - trunc f a) p₀ μ := trunc_compl_Lp_Lq_lower hp ⟨hp₀, hp₀p⟩ a_pos hf
@@ -2970,7 +2970,7 @@ lemma weaktype_estimate_trunc_top {C₁ : ℝ≥0} (hC₁ : C₁ > 0) {p p₁ q
29702970 have term_ne_top : (ENNReal.ofNNReal C₁) ^ p₁.toReal * eLpNorm f p μ ^ p.toReal ≠ ⊤ :=
29712971 mul_ne_top (rpow_ne_top' (ENNReal.coe_ne_zero.mpr hC₁.ne') coe_ne_top)
29722972 (rpow_ne_top' snorm_p_pos (MemLp.eLpNorm_ne_top hf))
2973- have d_pos : d > 0 := hdeq ▸ Real.rpow_pos_of_pos (zero_toReal ▸
2973+ have d_pos : d > 0 := hdeq ▸ Real.rpow_pos_of_pos (toReal_zero ▸
29742974 toReal_strict_mono term_ne_top term_pos) _
29752975 calc
29762976 _ ≤ ↑C₁ ^ p₁.toReal * ((ENNReal.ofReal (a ^ (p₁.toReal - p.toReal))) * eLpNorm f p μ ^ p.toReal) := by
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