analysis.ODE.gronwall ⟷ Mathlib.Analysis.ODE.Gronwall

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -77,7 +77,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
       (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
         ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using
       1
-    simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel' _ hK]
+    simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel₀ _ hK]
     ring
 #align has_deriv_at_gronwall_bound hasDerivAt_gronwallBound
 -/
@@ -178,7 +178,7 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_approx_trajectories_ODE_of_mem /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -231,7 +231,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_trajectories_ODE_of_mem /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -272,7 +272,7 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print ODE_solution_unique_of_mem_Icc_right /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -202,7 +202,7 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem {v : ℝ → E → E} {s : ℝ
   apply norm_le_gronwallBound_of_norm_deriv_right_le (hf.sub hg) h_deriv ha
   intro t ht
   have := dist_triangle4_right (f' t) (g' t) (v t (f t)) (v t (g t))
-  rw [dist_eq_norm] at this 
+  rw [dist_eq_norm] at this
   refine'
     this.trans
       ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht))
@@ -251,7 +251,7 @@ theorem dist_le_of_trajectories_ODE_of_mem {v : ℝ → E → E} {s : ℝ → Se
   have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros; rw [dist_self]
   intro t ht
   have := dist_le_of_approx_trajectories_ODE_of_mem hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
-  rwa [zero_add, gronwallBound_ε0] at this 
+  rwa [zero_add, gronwallBound_ε0] at this
 #align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem
 -/
 
@@ -286,7 +286,7 @@ theorem ODE_solution_unique_of_mem_Icc_right {v : ℝ → E → E} {s : ℝ →
   by
   intro t ht
   have := dist_le_of_trajectories_ODE_of_mem hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
-  rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
+  rwa [MulZeroClass.zero_mul, dist_le_zero] at this
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_Icc_right
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -179,14 +179,14 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
-#print dist_le_of_approx_trajectories_ODE_of_mem_set /-
+#print dist_le_of_approx_trajectories_ODE_of_mem /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
+theorem dist_le_of_approx_trajectories_ODE_of_mem {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
     (hv : ∀ t, ∀ (x) (_ : x ∈ s t) (y) (_ : y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
     {f g f' g' : ℝ → E} {a b : ℝ} {εf εg δ : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (f' t) (Ici t) t)
@@ -209,7 +209,7 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
             (hv t (f t) (hfs t ht) (g t) (hgs t ht))).trans
         _)
   rw [dist_eq_norm, add_comm]
-#align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem_set
+#align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem
 -/
 
 #print dist_le_of_approx_trajectories_ODE /-
@@ -226,20 +226,20 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
     (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ gronwallBound δ K (εf + εg) (t - a) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun t ht => trivial
-  dist_le_of_approx_trajectories_ODE_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf'
+  dist_le_of_approx_trajectories_ODE_of_mem (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf'
     f_bound hfs hg hg' g_bound (fun t ht => trivial) ha
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
-#print dist_le_of_trajectories_ODE_of_mem_set /-
+#print dist_le_of_trajectories_ODE_of_mem /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
+theorem dist_le_of_trajectories_ODE_of_mem {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
     (hv : ∀ t, ∀ (x) (_ : x ∈ s t) (y) (_ : y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
     {f g : ℝ → E} {a b : ℝ} {δ : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
@@ -250,10 +250,9 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
   have f_bound : ∀ t ∈ Ico a b, dist (v t (f t)) (v t (f t)) ≤ 0 := by intros; rw [dist_self]
   have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros; rw [dist_self]
   intro t ht
-  have :=
-    dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
+  have := dist_le_of_approx_trajectories_ODE_of_mem hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
   rwa [zero_add, gronwallBound_ε0] at this 
-#align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem_set
+#align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem
 -/
 
 #print dist_le_of_trajectories_ODE /-
@@ -268,17 +267,17 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
     (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun t ht => trivial
-  dist_le_of_trajectories_ODE_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg
-    hg' (fun t ht => trivial) ha
+  dist_le_of_trajectories_ODE_of_mem (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg hg'
+    (fun t ht => trivial) ha
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
-#print ODE_solution_unique_of_mem_set /-
+#print ODE_solution_unique_of_mem_Icc_right /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,
 and we consider only solutions included in `s`. -/
-theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
+theorem ODE_solution_unique_of_mem_Icc_right {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
     (hv : ∀ t, ∀ (x) (_ : x ∈ s t) (y) (_ : y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
     {f g : ℝ → E} {a b : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
@@ -286,9 +285,9 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : ∀ t ∈ Icc a b, f t = g t :=
   by
   intro t ht
-  have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
+  have := dist_le_of_trajectories_ODE_of_mem hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
   rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
-#align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
+#align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_Icc_right
 -/
 
 #print ODE_solution_unique /-
@@ -300,7 +299,7 @@ theorem ODE_solution_unique {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, Lip
     (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : f a = g a) :
     ∀ t ∈ Icc a b, f t = g t :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun t ht => trivial
-  ODE_solution_unique_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg hg'
+  ODE_solution_unique_of_mem_Icc_right (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg hg'
     (fun t ht => trivial) ha
 #align ODE_solution_unique ODE_solution_unique
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -97,8 +97,8 @@ theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
   by_cases hK : K = 0
   · simp only [gronwallBound, if_pos hK, MulZeroClass.mul_zero, add_zero]
   ·
-    simp only [gronwallBound, if_neg hK, MulZeroClass.mul_zero, exp_zero, sub_self, mul_one,
-      add_zero]
+    simp only [gronwallBound, if_neg hK, MulZeroClass.mul_zero, NormedSpace.exp_zero, sub_self,
+      mul_one, add_zero]
 #align gronwall_bound_x0 gronwallBound_x0
 -/
 
@@ -106,7 +106,7 @@ theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
 theorem gronwallBound_ε0 (δ K x : ℝ) : gronwallBound δ K 0 x = δ * exp (K * x) :=
   by
   by_cases hK : K = 0
-  · simp only [gronwallBound_K0, hK, MulZeroClass.zero_mul, exp_zero, add_zero, mul_one]
+  · simp only [gronwallBound_K0, hK, MulZeroClass.zero_mul, NormedSpace.exp_zero, add_zero, mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK, zero_div, MulZeroClass.zero_mul, add_zero]
 #align gronwall_bound_ε0 gronwallBound_ε0
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.SpecialFunctions.ExpDeriv
+import Analysis.SpecialFunctions.ExpDeriv
 
 #align_import analysis.ODE.gronwall from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
@@ -178,7 +178,7 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_approx_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -231,7 +231,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -273,7 +273,7 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print ODE_solution_unique_of_mem_set /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.ODE.gronwall
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.ExpDeriv
 
+#align_import analysis.ODE.gronwall from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # Grönwall's inequality
 
@@ -181,7 +178,7 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_approx_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -234,7 +231,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print dist_le_of_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
@@ -276,7 +273,7 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 #print ODE_solution_unique_of_mem_set /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -59,11 +59,14 @@ theorem gronwallBound_K0 (δ ε : ℝ) : gronwallBound δ 0 ε = fun x => δ + 
 #align gronwall_bound_K0 gronwallBound_K0
 -/
 
+#print gronwallBound_of_K_ne_0 /-
 theorem gronwallBound_of_K_ne_0 {δ K ε : ℝ} (hK : K ≠ 0) :
     gronwallBound δ K ε = fun x => δ * exp (K * x) + ε / K * (exp (K * x) - 1) :=
   funext fun x => if_neg hK
 #align gronwall_bound_of_K_ne_0 gronwallBound_of_K_ne_0
+-/
 
+#print hasDerivAt_gronwallBound /-
 theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
     HasDerivAt (gronwallBound δ K ε) (K * gronwallBound δ K ε x + ε) x :=
   by
@@ -80,6 +83,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
     simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel' _ hK]
     ring
 #align has_deriv_at_gronwall_bound hasDerivAt_gronwallBound
+-/
 
 #print hasDerivAt_gronwallBound_shift /-
 theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
@@ -101,16 +105,20 @@ theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
 #align gronwall_bound_x0 gronwallBound_x0
 -/
 
+#print gronwallBound_ε0 /-
 theorem gronwallBound_ε0 (δ K x : ℝ) : gronwallBound δ K 0 x = δ * exp (K * x) :=
   by
   by_cases hK : K = 0
   · simp only [gronwallBound_K0, hK, MulZeroClass.zero_mul, exp_zero, add_zero, mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK, zero_div, MulZeroClass.zero_mul, add_zero]
 #align gronwall_bound_ε0 gronwallBound_ε0
+-/
 
+#print gronwallBound_ε0_δ0 /-
 theorem gronwallBound_ε0_δ0 (K x : ℝ) : gronwallBound 0 K 0 x = 0 := by
   simp only [gronwallBound_ε0, MulZeroClass.zero_mul]
 #align gronwall_bound_ε0_δ0 gronwallBound_ε0_δ0
+-/
 
 #print gronwallBound_continuous_ε /-
 theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwallBound δ K ε x :=
@@ -126,6 +134,7 @@ theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwa
 /-! ### Inequality and corollaries -/
 
 
+#print le_gronwallBound_of_liminf_deriv_right_le /-
 /-- A Grönwall-like inequality: if `f : ℝ → ℝ` is continuous on `[a, b]` and satisfies
 the inequalities `f a ≤ δ` and
 `∀ x ∈ [a, b), liminf_{z→x+0} (f z - f x)/(z - x) ≤ K * (f x) + ε`, then `f x`
@@ -156,7 +165,9 @@ theorem le_gronwallBound_of_liminf_deriv_right_le {f f' : ℝ → ℝ} {δ K ε
   · simp only [closure_Ioi, left_mem_Ici]
   exact (gronwallBound_continuous_ε δ K (x - a)).ContinuousWithinAt
 #align le_gronwall_bound_of_liminf_deriv_right_le le_gronwallBound_of_liminf_deriv_right_le
+-/
 
+#print norm_le_gronwallBound_of_norm_deriv_right_le /-
 /-- A Grönwall-like inequality: if `f : ℝ → E` is continuous on `[a, b]`, has right derivative
 `f' x` at every point `x ∈ [a, b)`, and satisfies the inequalities `‖f a‖ ≤ δ`,
 `∀ x ∈ [a, b), ‖f' x‖ ≤ K * ‖f x‖ + ε`, then `‖f x‖` is bounded by `gronwall_bound δ K ε (x - a)`
@@ -168,8 +179,10 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
   le_gronwallBound_of_liminf_deriv_right_le (continuous_norm.comp_continuousOn hf)
     (fun x hx r hr => (hf' x hx).liminf_right_slope_norm_le hr) ha bound
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+#print dist_le_of_approx_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -200,7 +213,9 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
         _)
   rw [dist_eq_norm, add_comm]
 #align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem_set
+-/
 
+#print dist_le_of_approx_trajectories_ODE /-
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -217,8 +232,10 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
   dist_le_of_approx_trajectories_ODE_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf'
     f_bound hfs hg hg' g_bound (fun t ht => trivial) ha
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+#print dist_le_of_trajectories_ODE_of_mem_set /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -240,7 +257,9 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
     dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
   rwa [zero_add, gronwallBound_ε0] at this 
 #align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem_set
+-/
 
+#print dist_le_of_trajectories_ODE /-
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -255,8 +274,10 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
   dist_le_of_trajectories_ODE_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg
     hg' (fun t ht => trivial) ha
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+#print ODE_solution_unique_of_mem_set /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,
 and we consider only solutions included in `s`. -/
@@ -271,6 +292,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
   rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
+-/
 
 #print ODE_solution_unique /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) with

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -169,7 +169,7 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
     (fun x hx r hr => (hf' x hx).liminf_right_slope_norm_le hr) ha bound
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -218,7 +218,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
     f_bound hfs hg hg' g_bound (fun t ht => trivial) ha
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -256,7 +256,7 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
     hg' (fun t ht => trivial) ha
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,
 and we consider only solutions included in `s`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.ODE.gronwall
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecialFunctions.ExpDeriv
 /-!
 # Grönwall's inequality
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main technical result of this file is the Grönwall-like inequality
 `norm_le_gronwall_bound_of_norm_deriv_right_le`. It states that if `f : ℝ → E` satisfies `‖f a‖ ≤ δ`
 and `∀ x ∈ [a, b), ‖f' x‖ ≤ K * ‖f x‖ + ε`, then for all `x ∈ [a, b]` we have `‖f x‖ ≤ δ * exp (K *

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

@@ -43,14 +43,18 @@ open scoped Classical Topology NNReal
 /-! ### Technical lemmas about `gronwall_bound` -/
 
 
+#print gronwallBound /-
 /-- Upper bound used in several Grönwall-like inequalities. -/
 noncomputable def gronwallBound (δ K ε x : ℝ) : ℝ :=
   if K = 0 then δ + ε * x else δ * exp (K * x) + ε / K * (exp (K * x) - 1)
 #align gronwall_bound gronwallBound
+-/
 
+#print gronwallBound_K0 /-
 theorem gronwallBound_K0 (δ ε : ℝ) : gronwallBound δ 0 ε = fun x => δ + ε * x :=
   funext fun x => if_pos rfl
 #align gronwall_bound_K0 gronwallBound_K0
+-/
 
 theorem gronwallBound_of_K_ne_0 {δ K ε : ℝ} (hK : K ≠ 0) :
     gronwallBound δ K ε = fun x => δ * exp (K * x) + ε / K * (exp (K * x) - 1) :=
@@ -74,13 +78,16 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
     ring
 #align has_deriv_at_gronwall_bound hasDerivAt_gronwallBound
 
+#print hasDerivAt_gronwallBound_shift /-
 theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
     HasDerivAt (fun y => gronwallBound δ K ε (y - a)) (K * gronwallBound δ K ε (x - a) + ε) x :=
   by
   convert (hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a)
   rw [id, mul_one]
 #align has_deriv_at_gronwall_bound_shift hasDerivAt_gronwallBound_shift
+-/
 
+#print gronwallBound_x0 /-
 theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
   by
   by_cases hK : K = 0
@@ -89,6 +96,7 @@ theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
     simp only [gronwallBound, if_neg hK, MulZeroClass.mul_zero, exp_zero, sub_self, mul_one,
       add_zero]
 #align gronwall_bound_x0 gronwallBound_x0
+-/
 
 theorem gronwallBound_ε0 (δ K x : ℝ) : gronwallBound δ K 0 x = δ * exp (K * x) :=
   by
@@ -101,6 +109,7 @@ theorem gronwallBound_ε0_δ0 (K x : ℝ) : gronwallBound 0 K 0 x = 0 := by
   simp only [gronwallBound_ε0, MulZeroClass.zero_mul]
 #align gronwall_bound_ε0_δ0 gronwallBound_ε0_δ0
 
+#print gronwallBound_continuous_ε /-
 theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwallBound δ K ε x :=
   by
   by_cases hK : K = 0
@@ -109,6 +118,7 @@ theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwa
   · simp only [gronwallBound_of_K_ne_0 hK]
     exact continuous_const.add ((continuous_id.mul continuous_const).mul continuous_const)
 #align gronwall_bound_continuous_ε gronwallBound_continuous_ε
+-/
 
 /-! ### Inequality and corollaries -/
 
@@ -259,6 +269,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
   rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
 
+#print ODE_solution_unique /-
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) with
 a given initial value provided that RHS is Lipschitz continuous in `x`. -/
 theorem ODE_solution_unique {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, LipschitzWith K (v t))
@@ -270,4 +281,5 @@ theorem ODE_solution_unique {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, Lip
   ODE_solution_unique_of_mem_set (fun t x hx y hy => (hv t).dist_le_mul x y) hf hf' hfs hg hg'
     (fun t ht => trivial) ha
 #align ODE_solution_unique ODE_solution_unique
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -63,10 +63,11 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
   by_cases hK : K = 0
   · subst K
     simp only [gronwallBound_K0, MulZeroClass.zero_mul, zero_add]
-    convert((hasDerivAt_id x).const_mul ε).const_add δ
+    convert ((hasDerivAt_id x).const_mul ε).const_add δ
     rw [mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK]
-    convert(((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
+    convert
+      (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
         ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using
       1
     simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel' _ hK]
@@ -76,7 +77,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
 theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
     HasDerivAt (fun y => gronwallBound δ K ε (y - a)) (K * gronwallBound δ K ε (x - a) + ε) x :=
   by
-  convert(hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a)
+  convert (hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a)
   rw [id, mul_one]
 #align has_deriv_at_gronwall_bound_shift hasDerivAt_gronwallBound_shift
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -172,13 +172,13 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
     (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ gronwallBound δ K (εf + εg) (t - a) :=
   by
-  simp only [dist_eq_norm] at ha⊢
+  simp only [dist_eq_norm] at ha ⊢
   have h_deriv : ∀ t ∈ Ico a b, HasDerivWithinAt (fun t => f t - g t) (f' t - g' t) (Ici t) t :=
     fun t ht => (hf' t ht).sub (hg' t ht)
   apply norm_le_gronwallBound_of_norm_deriv_right_le (hf.sub hg) h_deriv ha
   intro t ht
   have := dist_triangle4_right (f' t) (g' t) (v t (f t)) (v t (g t))
-  rw [dist_eq_norm] at this
+  rw [dist_eq_norm] at this 
   refine'
     this.trans
       ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht))
@@ -219,12 +219,12 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) :=
   by
-  have f_bound : ∀ t ∈ Ico a b, dist (v t (f t)) (v t (f t)) ≤ 0 := by intros ; rw [dist_self]
-  have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros ; rw [dist_self]
+  have f_bound : ∀ t ∈ Ico a b, dist (v t (f t)) (v t (f t)) ≤ 0 := by intros; rw [dist_self]
+  have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros; rw [dist_self]
   intro t ht
   have :=
     dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
-  rwa [zero_add, gronwallBound_ε0] at this
+  rwa [zero_add, gronwallBound_ε0] at this 
 #align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem_set
 
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
@@ -255,7 +255,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
   by
   intro t ht
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
-  rwa [MulZeroClass.zero_mul, dist_le_zero] at this
+  rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
 
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) with

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -38,7 +38,7 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {F : Type _} [N
 
 open Metric Set Asymptotics Filter Real
 
-open Classical Topology NNReal
+open scoped Classical Topology NNReal
 
 /-! ### Technical lemmas about `gronwall_bound` -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -219,14 +219,8 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) :=
   by
-  have f_bound : ∀ t ∈ Ico a b, dist (v t (f t)) (v t (f t)) ≤ 0 :=
-    by
-    intros
-    rw [dist_self]
-  have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 :=
-    by
-    intros
-    rw [dist_self]
+  have f_bound : ∀ t ∈ Ico a b, dist (v t (f t)) (v t (f t)) ≤ 0 := by intros ; rw [dist_self]
+  have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros ; rw [dist_self]
   intro t ht
   have :=
     dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -63,11 +63,10 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
   by_cases hK : K = 0
   · subst K
     simp only [gronwallBound_K0, MulZeroClass.zero_mul, zero_add]
-    convert ((hasDerivAt_id x).const_mul ε).const_add δ
+    convert((hasDerivAt_id x).const_mul ε).const_add δ
     rw [mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK]
-    convert
-      (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
+    convert(((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
         ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using
       1
     simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel' _ hK]
@@ -77,7 +76,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
 theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
     HasDerivAt (fun y => gronwallBound δ K ε (y - a)) (K * gronwallBound δ K ε (x - a) + ε) x :=
   by
-  convert (hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a)
+  convert(hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a)
   rw [id, mul_one]
 #align has_deriv_at_gronwall_bound_shift hasDerivAt_gronwallBound_shift
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -62,7 +62,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
   by
   by_cases hK : K = 0
   · subst K
-    simp only [gronwallBound_K0, zero_mul, zero_add]
+    simp only [gronwallBound_K0, MulZeroClass.zero_mul, zero_add]
     convert ((hasDerivAt_id x).const_mul ε).const_add δ
     rw [mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK]
@@ -84,19 +84,21 @@ theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
 theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ :=
   by
   by_cases hK : K = 0
-  · simp only [gronwallBound, if_pos hK, mul_zero, add_zero]
-  · simp only [gronwallBound, if_neg hK, mul_zero, exp_zero, sub_self, mul_one, add_zero]
+  · simp only [gronwallBound, if_pos hK, MulZeroClass.mul_zero, add_zero]
+  ·
+    simp only [gronwallBound, if_neg hK, MulZeroClass.mul_zero, exp_zero, sub_self, mul_one,
+      add_zero]
 #align gronwall_bound_x0 gronwallBound_x0
 
 theorem gronwallBound_ε0 (δ K x : ℝ) : gronwallBound δ K 0 x = δ * exp (K * x) :=
   by
   by_cases hK : K = 0
-  · simp only [gronwallBound_K0, hK, zero_mul, exp_zero, add_zero, mul_one]
-  · simp only [gronwallBound_of_K_ne_0 hK, zero_div, zero_mul, add_zero]
+  · simp only [gronwallBound_K0, hK, MulZeroClass.zero_mul, exp_zero, add_zero, mul_one]
+  · simp only [gronwallBound_of_K_ne_0 hK, zero_div, MulZeroClass.zero_mul, add_zero]
 #align gronwall_bound_ε0 gronwallBound_ε0
 
 theorem gronwallBound_ε0_δ0 (K x : ℝ) : gronwallBound 0 K 0 x = 0 := by
-  simp only [gronwallBound_ε0, zero_mul]
+  simp only [gronwallBound_ε0, MulZeroClass.zero_mul]
 #align gronwall_bound_ε0_δ0 gronwallBound_ε0_δ0
 
 theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwallBound δ K ε x :=
@@ -260,7 +262,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
   by
   intro t ht
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
-  rwa [zero_mul, dist_le_zero] at this
+  rwa [MulZeroClass.zero_mul, dist_le_zero] at this
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
 
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) with

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -154,7 +154,7 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
     (fun x hx r hr => (hf' x hx).liminf_right_slope_norm_le hr) ha bound
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -203,7 +203,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
     f_bound hfs hg hg' g_bound (fun t ht => trivial) ha
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
@@ -247,7 +247,7 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
     hg' (fun t ht => trivial) ha
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s t) -/
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
 a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,
 and we consider only solutions included in `s`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -66,7 +66,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
   · simp only [gronwallBound_of_K_ne_0 hK]
     convert (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
       ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using 1
-    simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel' _ hK]
+    simp only [id, mul_add, (mul_assoc _ _ _).symm, mul_comm _ K, mul_div_cancel₀ _ hK]
     ring
 #align has_deriv_at_gronwall_bound hasDerivAt_gronwallBound
 

We prove the uniqueness of integral curves of a vector field on a manifold using the uniqueness theorem for solutions to ODEs.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -144,19 +144,24 @@ theorem norm_le_gronwallBound_of_norm_deriv_right_le {f f' : ℝ → E} {δ K ε
     (fun x hx _r hr => (hf' x hx).liminf_right_slope_norm_le hr) ha bound
 #align norm_le_gronwall_bound_of_norm_deriv_right_le norm_le_gronwallBound_of_norm_deriv_right_le
 
+variable {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0} {f g f' g' : ℝ → E} {a b t₀ : ℝ} {εf εg δ : ℝ}
+  (hv : ∀ t, LipschitzOnWith K (v t) (s t))
+
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
-    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
-    {f g f' g' : ℝ → E} {a b : ℝ} {εf εg δ : ℝ} (hf : ContinuousOn f (Icc a b))
+theorem dist_le_of_approx_trajectories_ODE_of_mem
+    (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (f' t) (Ici t) t)
-    (f_bound : ∀ t ∈ Ico a b, dist (f' t) (v t (f t)) ≤ εf) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
-    (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (g' t) (Ici t) t)
-    (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg) (hgs : ∀ t ∈ Ico a b, g t ∈ s t)
+    (f_bound : ∀ t ∈ Ico a b, dist (f' t) (v t (f t)) ≤ εf)
+    (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (g' t) (Ici t) t)
+    (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg)
+    (hgs : ∀ t ∈ Ico a b, g t ∈ s t)
     (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ gronwallBound δ K (εf + εg) (t - a) := by
   simp only [dist_eq_norm] at ha ⊢
@@ -170,22 +175,25 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
   refine this.trans ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht)) hv).trans ?_)
   rw [add_comm]
 set_option linter.uppercaseLean3 false in
-#align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem_set
+#align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem
 
 /-- If `f` and `g` are two approximate solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in the whole space. -/
-theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
-    (hv : ∀ t, LipschitzWith K (v t)) {f g f' g' : ℝ → E} {a b : ℝ} {εf εg δ : ℝ}
-    (hf : ContinuousOn f (Icc a b)) (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (f' t) (Ici t) t)
-    (f_bound : ∀ t ∈ Ico a b, dist (f' t) (v t (f t)) ≤ εf) (hg : ContinuousOn g (Icc a b))
+theorem dist_le_of_approx_trajectories_ODE
+    (hv : ∀ t, LipschitzWith K (v t))
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (f' t) (Ici t) t)
+    (f_bound : ∀ t ∈ Ico a b, dist (f' t) (v t (f t)) ≤ εf)
+    (hg : ContinuousOn g (Icc a b))
     (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (g' t) (Ici t) t)
-    (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg) (ha : dist (f a) (g a) ≤ δ) :
+    (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg)
+    (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ gronwallBound δ K (εf + εg) (t - a) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  dist_le_of_approx_trajectories_ODE_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf'
+  dist_le_of_approx_trajectories_ODE_of_mem (fun t => (hv t).lipschitzOnWith _) hf hf'
     f_bound hfs hg hg' g_bound (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
@@ -196,10 +204,10 @@ people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
-    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
-    {f g : ℝ → E} {a b : ℝ} {δ : ℝ} (hf : ContinuousOn f (Icc a b))
-    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
+theorem dist_le_of_trajectories_ODE_of_mem
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t)
+    (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
     (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) := by
@@ -207,23 +215,26 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
   have g_bound : ∀ t ∈ Ico a b, dist (v t (g t)) (v t (g t)) ≤ 0 := by intros; rw [dist_self]
   intro t ht
   have :=
-    dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
+    dist_le_of_approx_trajectories_ODE_of_mem hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
   rwa [zero_add, gronwallBound_ε0] at this
 set_option linter.uppercaseLean3 false in
-#align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem_set
+#align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem
 
 /-- If `f` and `g` are two exact solutions of the same ODE, then the distance between them
 can't grow faster than exponentially. This is a simple corollary of Grönwall's inequality, and some
 people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in the whole space. -/
-theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, LipschitzWith K (v t))
-    {f g : ℝ → E} {a b : ℝ} {δ : ℝ} (hf : ContinuousOn f (Icc a b))
-    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hg : ContinuousOn g (Icc a b))
-    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : dist (f a) (g a) ≤ δ) :
+theorem dist_le_of_trajectories_ODE
+    (hv : ∀ t, LipschitzWith K (v t))
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
+    (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  dist_le_of_trajectories_ODE_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg
+  dist_le_of_trajectories_ODE_of_mem (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg
     hg' (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
@@ -233,26 +244,137 @@ a given initial value provided that the RHS is Lipschitz continuous in `x` withi
 and we consider only solutions included in `s`.
 
 This version shows uniqueness in a closed interval `Icc a b`, where `a` is the initial time. -/
-theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
-    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
-    {f g : ℝ → E} {a b : ℝ} (hf : ContinuousOn f (Icc a b))
-    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
-    (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
-    (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : EqOn f g (Icc a b) := fun t ht ↦ by
-  have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
+theorem ODE_solution_unique_of_mem_Icc_right
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t)
+    (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
+    (hgs : ∀ t ∈ Ico a b, g t ∈ s t)
+    (ha : f a = g a) :
+    EqOn f g (Icc a b) := fun t ht ↦ by
+  have := dist_le_of_trajectories_ODE_of_mem hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
   rwa [zero_mul, dist_le_zero] at this
 set_option linter.uppercaseLean3 false in
-#align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
+#align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_Icc_right
+
+/-- A time-reversed version of `ODE_solution_unique_of_mem_Icc_right`. Uniqueness is shown in a
+closed interval `Icc a b`, where `b` is the "initial" time. -/
+theorem ODE_solution_unique_of_mem_Icc_left
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ioc a b, HasDerivWithinAt f (v t (f t)) (Iic t) t)
+    (hfs : ∀ t ∈ Ioc a b, f t ∈ s t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ioc a b, HasDerivWithinAt g (v t (g t)) (Iic t) t)
+    (hgs : ∀ t ∈ Ioc a b, g t ∈ s t)
+    (hb : f b = g b) :
+    EqOn f g (Icc a b) := by
+  have hv' t : LipschitzOnWith K (Neg.neg ∘ (v (-t))) (s (-t)) := by
+    rw [← one_mul K]
+    exact LipschitzWith.id.neg.comp_lipschitzOnWith (hv _)
+  have hmt1 : MapsTo Neg.neg (Icc (-b) (-a)) (Icc a b) :=
+    fun _ ht ↦ ⟨le_neg.mp ht.2, neg_le.mp ht.1⟩
+  have hmt2 : MapsTo Neg.neg (Ico (-b) (-a)) (Ioc a b) :=
+    fun _ ht ↦ ⟨lt_neg.mp ht.2, neg_le.mp ht.1⟩
+  have hmt3 (t : ℝ) : MapsTo Neg.neg (Ici t) (Iic (-t)) :=
+    fun _ ht' ↦ mem_Iic.mpr <| neg_le_neg ht'
+  suffices EqOn (f ∘ Neg.neg) (g ∘ Neg.neg) (Icc (-b) (-a)) by
+    rw [eqOn_comp_right_iff] at this
+    convert this
+    simp
+  apply ODE_solution_unique_of_mem_Icc_right hv'
+    (hf.comp continuousOn_neg hmt1) _ (fun _ ht ↦ hfs _ (hmt2 ht))
+    (hg.comp continuousOn_neg hmt1) _ (fun _ ht ↦ hgs _ (hmt2 ht)) (by simp [hb])
+  · intros t ht
+    convert HasFDerivWithinAt.comp_hasDerivWithinAt t (hf' (-t) (hmt2 ht))
+      (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
+    simp
+  · intros t ht
+    convert HasFDerivWithinAt.comp_hasDerivWithinAt t (hg' (-t) (hmt2 ht))
+      (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
+    simp
+
+/-- A version of `ODE_solution_unique_of_mem_Icc_right` for uniqueness in a closed interval whose
+interior contains the initial time. -/
+theorem ODE_solution_unique_of_mem_Icc
+    (ht : t₀ ∈ Ioo a b)
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ioo a b, HasDerivAt f (v t (f t)) t)
+    (hfs : ∀ t ∈ Ioo a b, f t ∈ s t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ioo a b, HasDerivAt g (v t (g t)) t)
+    (hgs : ∀ t ∈ Ioo a b, g t ∈ s t)
+    (heq : f t₀ = g t₀) :
+    EqOn f g (Icc a b) := by
+  rw [← Icc_union_Icc_eq_Icc (le_of_lt ht.1) (le_of_lt ht.2)]
+  apply EqOn.union
+  · have hss : Ioc a t₀ ⊆ Ioo a b := Ioc_subset_Ioo_right ht.2
+    exact ODE_solution_unique_of_mem_Icc_left hv
+      (hf.mono <| Icc_subset_Icc_right <| le_of_lt ht.2)
+      (fun _ ht' ↦ (hf' _ (hss ht')).hasDerivWithinAt) (fun _ ht' ↦ (hfs _ (hss ht')))
+      (hg.mono <| Icc_subset_Icc_right <| le_of_lt ht.2)
+      (fun _ ht' ↦ (hg' _ (hss ht')).hasDerivWithinAt) (fun _ ht' ↦ (hgs _ (hss ht'))) heq
+  · have hss : Ico t₀ b ⊆ Ioo a b := Ico_subset_Ioo_left ht.1
+    exact ODE_solution_unique_of_mem_Icc_right hv
+      (hf.mono <| Icc_subset_Icc_left <| le_of_lt ht.1)
+      (fun _ ht' ↦ (hf' _ (hss ht')).hasDerivWithinAt) (fun _ ht' ↦ (hfs _ (hss ht')))
+      (hg.mono <| Icc_subset_Icc_left <| le_of_lt ht.1)
+      (fun _ ht' ↦ (hg' _ (hss ht')).hasDerivWithinAt) (fun _ ht' ↦ (hgs _ (hss ht'))) heq
+
+/-- A version of `ODE_solution_unique_of_mem_Icc` for uniqueness in an open interval. -/
+theorem ODE_solution_unique_of_mem_Ioo
+    (ht : t₀ ∈ Ioo a b)
+    (hf : ∀ t ∈ Ioo a b, HasDerivAt f (v t (f t)) t ∧ f t ∈ s t)
+    (hg : ∀ t ∈ Ioo a b, HasDerivAt g (v t (g t)) t ∧ g t ∈ s t)
+    (heq : f t₀ = g t₀) :
+    EqOn f g (Ioo a b) := by
+  intros t' ht'
+  rcases lt_or_le t' t₀ with (h | h)
+  · have hss : Icc t' t₀ ⊆ Ioo a b :=
+      fun _ ht'' ↦ ⟨lt_of_lt_of_le ht'.1 ht''.1, lt_of_le_of_lt ht''.2 ht.2⟩
+    exact ODE_solution_unique_of_mem_Icc_left hv
+      (ContinuousAt.continuousOn fun _ ht'' ↦ (hf _ <| hss ht'').1.continuousAt)
+      (fun _ ht'' ↦ (hf _ <| hss <| Ioc_subset_Icc_self ht'').1.hasDerivWithinAt)
+      (fun _ ht'' ↦ (hf _ <| hss <| Ioc_subset_Icc_self ht'').2)
+      (ContinuousAt.continuousOn fun _ ht'' ↦ (hg _ <| hss ht'').1.continuousAt)
+      (fun _ ht'' ↦ (hg _ <| hss <| Ioc_subset_Icc_self ht'').1.hasDerivWithinAt)
+      (fun _ ht'' ↦ (hg _ <| hss <| Ioc_subset_Icc_self ht'').2) heq
+      ⟨le_rfl, le_of_lt h⟩
+  · have hss : Icc t₀ t' ⊆ Ioo a b :=
+      fun _ ht'' ↦ ⟨lt_of_lt_of_le ht.1 ht''.1, lt_of_le_of_lt ht''.2 ht'.2⟩
+    exact ODE_solution_unique_of_mem_Icc_right hv
+      (ContinuousAt.continuousOn fun _ ht'' ↦ (hf _ <| hss ht'').1.continuousAt)
+      (fun _ ht'' ↦ (hf _ <| hss <| Ico_subset_Icc_self ht'').1.hasDerivWithinAt)
+      (fun _ ht'' ↦ (hf _ <| hss <| Ico_subset_Icc_self ht'').2)
+      (ContinuousAt.continuousOn fun _ ht'' ↦ (hg _ <| hss ht'').1.continuousAt)
+      (fun _ ht'' ↦ (hg _ <| hss <| Ico_subset_Icc_self ht'').1.hasDerivWithinAt)
+      (fun _ ht'' ↦ (hg _ <| hss <| Ico_subset_Icc_self ht'').2) heq
+      ⟨h, le_rfl⟩
+
+/-- Local unqueness of ODE solutions. -/
+theorem ODE_solution_unique_of_eventually
+    (hf : ∀ᶠ t in 𝓝 t₀, HasDerivAt f (v t (f t)) t ∧ f t ∈ s t)
+    (hg : ∀ᶠ t in 𝓝 t₀, HasDerivAt g (v t (g t)) t ∧ g t ∈ s t)
+    (heq : f t₀ = g t₀) : f =ᶠ[𝓝 t₀] g := by
+  obtain ⟨ε, hε, h⟩ := eventually_nhds_iff_ball.mp (hf.and hg)
+  rw [Filter.eventuallyEq_iff_exists_mem]
+  refine ⟨ball t₀ ε, ball_mem_nhds _ hε, ?_⟩
+  simp_rw [Real.ball_eq_Ioo] at *
+  apply ODE_solution_unique_of_mem_Ioo hv (Real.ball_eq_Ioo t₀ ε ▸ mem_ball_self hε)
+    (fun _ ht ↦ (h _ ht).1) (fun _ ht ↦ (h _ ht).2) heq
 
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) with
-a given initial value provided that RHS is Lipschitz continuous in `x`. -/
-theorem ODE_solution_unique {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, LipschitzWith K (v t))
-    {f g : ℝ → E} {a b : ℝ} (hf : ContinuousOn f (Icc a b))
-    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hg : ContinuousOn g (Icc a b))
-    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : f a = g a) :
+a given initial value provided that the RHS is Lipschitz continuous in `x`. -/
+theorem ODE_solution_unique
+    (hv : ∀ t, LipschitzWith K (v t))
+    (hf : ContinuousOn f (Icc a b))
+    (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t)
+    (hg : ContinuousOn g (Icc a b))
+    (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
+    (ha : f a = g a) :
     EqOn f g (Icc a b) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  ODE_solution_unique_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg hg'
+  ODE_solution_unique_of_mem_Icc_right (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg hg'
     (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align ODE_solution_unique ODE_solution_unique

Restate the uniqueness theorems for solutions to ODEs using LipschitzOnWith and EqOn rather than the equivalent raw propositions, so that relevant APIs may be used for arguments of these theorems.

@@ -150,8 +150,8 @@ people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
-    (hv : ∀ t, ∀ᵉ (x ∈ s t) (y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
+theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
+    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
     {f g f' g' : ℝ → E} {a b : ℝ} {εf εg δ : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (f' t) (Ici t) t)
     (f_bound : ∀ t ∈ Ico a b, dist (f' t) (v t (f t)) ≤ εf) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
@@ -165,10 +165,10 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
   apply norm_le_gronwallBound_of_norm_deriv_right_le (hf.sub hg) h_deriv ha
   intro t ht
   have := dist_triangle4_right (f' t) (g' t) (v t (f t)) (v t (g t))
-  rw [dist_eq_norm] at this
-  refine' this.trans ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht))
-    (hv t (f t) (hfs t ht) (g t) (hgs t ht))).trans _)
-  rw [dist_eq_norm, add_comm]
+  have hv := (hv t).dist_le_mul _ (hfs t ht) _ (hgs t ht)
+  rw [← dist_eq_norm, ← dist_eq_norm]
+  refine this.trans ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht)) hv).trans ?_)
+  rw [add_comm]
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_approx_trajectories_ODE_of_mem_set dist_le_of_approx_trajectories_ODE_of_mem_set
 
@@ -185,7 +185,7 @@ theorem dist_le_of_approx_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0}
     (g_bound : ∀ t ∈ Ico a b, dist (g' t) (v t (g t)) ≤ εg) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ gronwallBound δ K (εf + εg) (t - a) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  dist_le_of_approx_trajectories_ODE_of_mem_set (fun t x _ y _ => (hv t).dist_le_mul x y) hf hf'
+  dist_le_of_approx_trajectories_ODE_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf'
     f_bound hfs hg hg' g_bound (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_approx_trajectories_ODE dist_le_of_approx_trajectories_ODE
@@ -196,8 +196,8 @@ people call this Grönwall's inequality too.
 
 This version assumes all inequalities to be true in some time-dependent set `s t`,
 and assumes that the solutions never leave this set. -/
-theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
-    (hv : ∀ t, ∀ᵉ (x ∈ s t) (y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
+theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
+    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
     {f g : ℝ → E} {a b : ℝ} {δ : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
     (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
@@ -223,20 +223,22 @@ theorem dist_le_of_trajectories_ODE {v : ℝ → E → E} {K : ℝ≥0} (hv : 
     (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : dist (f a) (g a) ≤ δ) :
     ∀ t ∈ Icc a b, dist (f t) (g t) ≤ δ * exp (K * (t - a)) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  dist_le_of_trajectories_ODE_of_mem_set (fun t x _ y _ => (hv t).dist_le_mul x y) hf hf' hfs hg
+  dist_le_of_trajectories_ODE_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg
     hg' (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_trajectories_ODE dist_le_of_trajectories_ODE
 
 /-- There exists only one solution of an ODE \(\dot x=v(t, x)\) in a set `s ⊆ ℝ × E` with
-a given initial value provided that RHS is Lipschitz continuous in `x` within `s`,
-and we consider only solutions included in `s`. -/
-theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ}
-    (hv : ∀ t, ∀ᵉ (x ∈ s t) (y ∈ s t), dist (v t x) (v t y) ≤ K * dist x y)
+a given initial value provided that the RHS is Lipschitz continuous in `x` within `s`,
+and we consider only solutions included in `s`.
+
+This version shows uniqueness in a closed interval `Icc a b`, where `a` is the initial time. -/
+theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E} {K : ℝ≥0}
+    (hv : ∀ t, LipschitzOnWith K (v t) (s t))
     {f g : ℝ → E} {a b : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hfs : ∀ t ∈ Ico a b, f t ∈ s t)
     (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
-    (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : ∀ t ∈ Icc a b, f t = g t := fun t ht ↦ by
+    (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : EqOn f g (Icc a b) := fun t ht ↦ by
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
   rwa [zero_mul, dist_le_zero] at this
 set_option linter.uppercaseLean3 false in
@@ -248,10 +250,9 @@ theorem ODE_solution_unique {v : ℝ → E → E} {K : ℝ≥0} (hv : ∀ t, Lip
     {f g : ℝ → E} {a b : ℝ} (hf : ContinuousOn f (Icc a b))
     (hf' : ∀ t ∈ Ico a b, HasDerivWithinAt f (v t (f t)) (Ici t) t) (hg : ContinuousOn g (Icc a b))
     (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t) (ha : f a = g a) :
-    ∀ t ∈ Icc a b, f t = g t :=
+    EqOn f g (Icc a b) :=
   have hfs : ∀ t ∈ Ico a b, f t ∈ @univ E := fun _ _ => trivial
-  ODE_solution_unique_of_mem_set (fun t x _ y _ => (hv t).dist_le_mul x y) hf hf' hfs hg hg'
+  ODE_solution_unique_of_mem_set (fun t => (hv t).lipschitzOnWith _) hf hf' hfs hg hg'
     (fun _ _ => trivial) ha
 set_option linter.uppercaseLean3 false in
 #align ODE_solution_unique ODE_solution_unique
-

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -60,7 +60,7 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
     HasDerivAt (gronwallBound δ K ε) (K * gronwallBound δ K ε x + ε) x := by
   by_cases hK : K = 0
   · subst K
-    simp only [gronwallBound_K0, MulZeroClass.zero_mul, zero_add]
+    simp only [gronwallBound_K0, zero_mul, zero_add]
     convert ((hasDerivAt_id x).const_mul ε).const_add δ
     rw [mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK]
@@ -78,19 +78,19 @@ theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
 
 theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ := by
   by_cases hK : K = 0
-  · simp only [gronwallBound, if_pos hK, MulZeroClass.mul_zero, add_zero]
-  · simp only [gronwallBound, if_neg hK, MulZeroClass.mul_zero, exp_zero, sub_self, mul_one,
+  · simp only [gronwallBound, if_pos hK, mul_zero, add_zero]
+  · simp only [gronwallBound, if_neg hK, mul_zero, exp_zero, sub_self, mul_one,
       add_zero]
 #align gronwall_bound_x0 gronwallBound_x0
 
 theorem gronwallBound_ε0 (δ K x : ℝ) : gronwallBound δ K 0 x = δ * exp (K * x) := by
   by_cases hK : K = 0
-  · simp only [gronwallBound_K0, hK, MulZeroClass.zero_mul, exp_zero, add_zero, mul_one]
-  · simp only [gronwallBound_of_K_ne_0 hK, zero_div, MulZeroClass.zero_mul, add_zero]
+  · simp only [gronwallBound_K0, hK, zero_mul, exp_zero, add_zero, mul_one]
+  · simp only [gronwallBound_of_K_ne_0 hK, zero_div, zero_mul, add_zero]
 #align gronwall_bound_ε0 gronwallBound_ε0
 
 theorem gronwallBound_ε0_δ0 (K x : ℝ) : gronwallBound 0 K 0 x = 0 := by
-  simp only [gronwallBound_ε0, MulZeroClass.zero_mul]
+  simp only [gronwallBound_ε0, zero_mul]
 #align gronwall_bound_ε0_δ0 gronwallBound_ε0_δ0
 
 theorem gronwallBound_continuous_ε (δ K x : ℝ) : Continuous fun ε => gronwallBound δ K ε x := by
@@ -238,7 +238,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
     (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : ∀ t ∈ Icc a b, f t = g t := fun t ht ↦ by
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
-  rwa [MulZeroClass.zero_mul, dist_le_zero] at this
+  rwa [zero_mul, dist_le_zero] at this
 set_option linter.uppercaseLean3 false in
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
 

@@ -165,7 +165,7 @@ theorem dist_le_of_approx_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s :
   apply norm_le_gronwallBound_of_norm_deriv_right_le (hf.sub hg) h_deriv ha
   intro t ht
   have := dist_triangle4_right (f' t) (g' t) (v t (f t)) (v t (g t))
-  rw [dist_eq_norm] at this 
+  rw [dist_eq_norm] at this
   refine' this.trans ((add_le_add (add_le_add (f_bound t ht) (g_bound t ht))
     (hv t (f t) (hfs t ht) (g t) (hgs t ht))).trans _)
   rw [dist_eq_norm, add_comm]
@@ -208,7 +208,7 @@ theorem dist_le_of_trajectories_ODE_of_mem_set {v : ℝ → E → E} {s : ℝ 
   intro t ht
   have :=
     dist_le_of_approx_trajectories_ODE_of_mem_set hv hf hf' f_bound hfs hg hg' g_bound hgs ha t ht
-  rwa [zero_add, gronwallBound_ε0] at this 
+  rwa [zero_add, gronwallBound_ε0] at this
 set_option linter.uppercaseLean3 false in
 #align dist_le_of_trajectories_ODE_of_mem_set dist_le_of_trajectories_ODE_of_mem_set
 
@@ -238,7 +238,7 @@ theorem ODE_solution_unique_of_mem_set {v : ℝ → E → E} {s : ℝ → Set E}
     (hg : ContinuousOn g (Icc a b)) (hg' : ∀ t ∈ Ico a b, HasDerivWithinAt g (v t (g t)) (Ici t) t)
     (hgs : ∀ t ∈ Ico a b, g t ∈ s t) (ha : f a = g a) : ∀ t ∈ Icc a b, f t = g t := fun t ht ↦ by
   have := dist_le_of_trajectories_ODE_of_mem_set hv hf hf' hfs hg hg' hgs (dist_le_zero.2 ha) t ht
-  rwa [MulZeroClass.zero_mul, dist_le_zero] at this 
+  rwa [MulZeroClass.zero_mul, dist_le_zero] at this
 set_option linter.uppercaseLean3 false in
 #align ODE_solution_unique_of_mem_set ODE_solution_unique_of_mem_set
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -30,7 +30,7 @@ Sec. 4.5][HubbardWest-ode], where `norm_le_gronwallBound_of_norm_deriv_right_le`
 -/
 
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {F : Type _} [NormedAddCommGroup F]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {F : Type*} [NormedAddCommGroup F]
   [NormedSpace ℝ F]
 
 open Metric Set Asymptotics Filter Real

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.ODE.gronwall
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.ExpDeriv
 
+#align_import analysis.ODE.gronwall from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Grönwall's inequality