diff --git a/theories/charge.v b/theories/charge.v index e1f9965f94..9fae017ba9 100644 --- a/theories/charge.v +++ b/theories/charge.v @@ -91,7 +91,6 @@ Unset Strict Implicit. Unset Printing Implicit Defensive. Import Order.TTheory GRing.Theory Num.Def Num.Theory. -Import numFieldTopology.Exports. Import numFieldNormedType.Exports. Local Open Scope ring_scope. diff --git a/theories/ftc.v b/theories/ftc.v index 2d944d434e..9b3d9fc48a 100644 --- a/theories/ftc.v +++ b/theories/ftc.v @@ -24,7 +24,6 @@ Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import Order.TTheory GRing.Theory Num.Def Num.Theory. -Import numFieldTopology.Exports. Import numFieldNormedType.Exports. Local Open Scope classical_set_scope. @@ -39,7 +38,7 @@ Implicit Types (f : R -> R) (a : itv_bound R). Let FTC0 f a : mu.-integrable setT (EFin \o f) -> let F x := (\int[mu]_(t in [set` Interval a (BRight x)]) f t)%R in forall x, a < BRight x -> lebesgue_pt f x -> - h^-1 *: (F (h + x) - F x) @[h --> (0:R)%R^'] --> f x. + h^-1 *: (F (h + x) - F x) @[h --> 0%R^'] --> f x. Proof. move=> intf F x ax fx. have locf : locally_integrable setT f. @@ -191,7 +190,7 @@ Let FTC0_restrict f a x (u : R) : (x < u)%R -> mu.-integrable [set` Interval a (BRight u)] (EFin \o f) -> let F y := (\int[mu]_(t in [set` Interval a (BRight y)]) f t)%R in a < BRight x -> lebesgue_pt f x -> - h^-1 *: (F (h + x) - F x) @[h --> ((0:R)%R^')] --> f x. + h^-1 *: (F (h + x) - F x) @[h --> (0%R^')] --> f x. Proof. move=> xu + F ax fx. rewrite integrable_mkcond//= (restrict_EFin f) => intf. @@ -354,7 +353,7 @@ Unshelve. all: by end_near. Qed. Lemma parameterized_integral_cvg_left a b (f : R -> R) : a < b -> mu.-integrable `[a, b] (EFin \o f) -> - int a x f @[x --> a] --> (0:R). + int a x f @[x --> a] --> 0. Proof. move=> ab intf; pose fab := f \_ `[a, b]. have intfab : mu.-integrable `[a, b] (EFin \o fab). diff --git a/theories/lebesgue_integral.v b/theories/lebesgue_integral.v index 28b581bd6a..e743cd0a71 100644 --- a/theories/lebesgue_integral.v +++ b/theories/lebesgue_integral.v @@ -82,7 +82,6 @@ Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import Order.TTheory GRing.Theory Num.Def Num.Theory. -Import numFieldTopology.Exports. Import numFieldNormedType.Exports. From mathcomp Require Import mathcomp_extra. diff --git a/theories/lebesgue_measure.v b/theories/lebesgue_measure.v index bdd6263f30..193331cbad 100644 --- a/theories/lebesgue_measure.v +++ b/theories/lebesgue_measure.v @@ -61,7 +61,6 @@ Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import Order.TTheory GRing.Theory Num.Def Num.Theory. -Import numFieldTopology.Exports. Import numFieldNormedType.Exports. Local Open Scope classical_set_scope.