diff options
author | 2003-04-10 21:55:33 +0000 | |
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committer | 2003-04-10 21:55:33 +0000 | |
commit | 0acce1966cdcaa7b196150bc4f48e841cb82dc16 (patch) | |
tree | 3552ee3e82f12ea6fad80534b4fc82c95969ba63 | |
parent | 463531101b7db0a47c49242346f6e765b3cec3b4 (diff) |
Remplacement Import par Open Scope en v8
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3909 85f007b7-540e-0410-9357-904b9bb8a0f7
44 files changed, 47 insertions, 47 deletions
diff --git a/theories/Reals/Alembert.v b/theories/Reals/Alembert.v index 36131beb0..60ab7b6cf 100644 --- a/theories/Reals/Alembert.v +++ b/theories/Reals/Alembert.v @@ -14,7 +14,7 @@ Require Rseries. Require SeqProp. Require PartSum. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (***************************************************) (* Various versions of the criterion of D'Alembert *) diff --git a/theories/Reals/AltSeries.v b/theories/Reals/AltSeries.v index 7047bb03d..8de35273d 100644 --- a/theories/Reals/AltSeries.v +++ b/theories/Reals/AltSeries.v @@ -14,7 +14,7 @@ Require Rseries. Require SeqProp. Require PartSum. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Definition tg_alt [Un:nat->R] : nat->R := [i:nat]``(pow (-1) i)*(Un i)``. diff --git a/theories/Reals/ArithProp.v b/theories/Reals/ArithProp.v index 62d160934..51970655a 100644 --- a/theories/Reals/ArithProp.v +++ b/theories/Reals/ArithProp.v @@ -12,7 +12,7 @@ Require Rbase. Require Rbasic_fun. Require Even. Require Div2. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma minus_neq_O : (n,i:nat) (lt i n) -> ~(minus n i)=O. Intros; Red; Intro. diff --git a/theories/Reals/Binomial.v b/theories/Reals/Binomial.v index 03b6b46fc..c90f121a9 100644 --- a/theories/Reals/Binomial.v +++ b/theories/Reals/Binomial.v @@ -11,7 +11,7 @@ Require Rbase. Require Rfunctions. Require PartSum. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition C [n,p:nat] : R := ``(INR (fact n))/((INR (fact p))*(INR (fact (minus n p))))``. diff --git a/theories/Reals/Cauchy_prod.v b/theories/Reals/Cauchy_prod.v index 5cd8bf672..bbb3c3396 100644 --- a/theories/Reals/Cauchy_prod.v +++ b/theories/Reals/Cauchy_prod.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Rseries. Require PartSum. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Lemma sum_N_predN : (An:nat->R;N:nat) (lt O N) -> (sum_f_R0 An N)==``(sum_f_R0 An (pred N)) + (An N)``. diff --git a/theories/Reals/Cos_plus.v b/theories/Reals/Cos_plus.v index ae650225f..c89787feb 100644 --- a/theories/Reals/Cos_plus.v +++ b/theories/Reals/Cos_plus.v @@ -14,8 +14,8 @@ Require SeqSeries. Require Rtrigo_def. Require Cos_rel. Require Max. -V7only [Import nat_scope.]. -V7only [Import R_scope.]. +V7only [Import nat_scope.]. Open Scope nat_scope. +V7only [Import R_scope.]. Open Scope R_scope. Definition Majxy [x,y:R] : nat->R := [n:nat](Rdiv (pow (Rmax R1 (Rmax (Rabsolu x) (Rabsolu y))) (mult (4) (S n))) (INR (fact n))). diff --git a/theories/Reals/Cos_rel.v b/theories/Reals/Cos_rel.v index b773057ed..5196cba38 100644 --- a/theories/Reals/Cos_rel.v +++ b/theories/Reals/Cos_rel.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require SeqSeries. Require Rtrigo_def. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition A1 [x:R] : nat->R := [N:nat](sum_f_R0 [k:nat]``(pow (-1) k)/(INR (fact (mult (S (S O)) k)))*(pow x (mult (S (S O)) k))`` N). diff --git a/theories/Reals/DiscrR.v b/theories/Reals/DiscrR.v index 62bf0265d..66a66f399 100644 --- a/theories/Reals/DiscrR.v +++ b/theories/Reals/DiscrR.v @@ -10,7 +10,7 @@ Require RIneq. Require Omega. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma Rlt_R0_R2 : ``0<2``. Replace ``2`` with (INR (2)); [Apply lt_INR_0; Apply lt_O_Sn | Reflexivity]. diff --git a/theories/Reals/Exp_prop.v b/theories/Reals/Exp_prop.v index ca5de937b..34c9a2c50 100644 --- a/theories/Reals/Exp_prop.v +++ b/theories/Reals/Exp_prop.v @@ -17,7 +17,7 @@ Require PSeries_reg. Require Div2. Require Even. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition E1 [x:R] : nat->R := [N:nat](sum_f_R0 [k:nat]``/(INR (fact k))*(pow x k)`` N). diff --git a/theories/Reals/MVT.v b/theories/Reals/MVT.v index 7de5c64c0..3f06c65d8 100644 --- a/theories/Reals/MVT.v +++ b/theories/Reals/MVT.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Ranalysis1. Require Rtopology. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (* The Mean Value Theorem *) Theorem MVT : (f,g:R->R;a,b:R;pr1:(c:R)``a<c<b``->(derivable_pt f c);pr2:(c:R)``a<c<b``->(derivable_pt g c)) ``a<b`` -> ((c:R)``a<=c<=b``->(continuity_pt f c)) -> ((c:R)``a<=c<=b``->(continuity_pt g c)) -> (EXT c : R | (EXT P : ``a<c<b`` | ``((g b)-(g a))*(derive_pt f c (pr1 c P))==((f b)-(f a))*(derive_pt g c (pr2 c P))``)). diff --git a/theories/Reals/NewtonInt.v b/theories/Reals/NewtonInt.v index 7c7cb59ea..5878481a5 100644 --- a/theories/Reals/NewtonInt.v +++ b/theories/Reals/NewtonInt.v @@ -13,7 +13,7 @@ Require Rfunctions. Require SeqSeries. Require Rtrigo. Require Ranalysis. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*******************************************) (* Newton's Integral *) diff --git a/theories/Reals/PSeries_reg.v b/theories/Reals/PSeries_reg.v index 8a4aa1fc5..422cbcf6a 100644 --- a/theories/Reals/PSeries_reg.v +++ b/theories/Reals/PSeries_reg.v @@ -14,7 +14,7 @@ Require SeqSeries. Require Ranalysis1. Require Max. Require Even. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition Boule [x:R;r:posreal] : R -> Prop := [y:R]``(Rabsolu (y-x))<r``. diff --git a/theories/Reals/PartSum.v b/theories/Reals/PartSum.v index 66d3496d3..7f6bd9177 100644 --- a/theories/Reals/PartSum.v +++ b/theories/Reals/PartSum.v @@ -13,7 +13,7 @@ Require Rfunctions. Require Rseries. Require Rcomplete. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma tech1 : (An:nat->R;N:nat) ((n:nat)``(le n N)``->``0<(An n)``) -> ``0 < (sum_f_R0 An N)``. Intros; Induction N. diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 0f57c281d..025eb5410 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -16,9 +16,9 @@ Require Export Raxioms. Require Export ZArithRing. Require Omega. Require Export Field. -V7only [Import nat_scope.]. -V7only [Import Z_scope.]. -V7only [Import R_scope.]. +V7only [Import nat_scope.]. Open Scope nat_scope. +V7only [Import Z_scope.]. Open Scope Z_scope. +V7only [Import R_scope.]. Open Scope R_scope. Implicit Variable Type r:R. diff --git a/theories/Reals/RList.v b/theories/Reals/RList.v index edfb48728..00563ebcd 100644 --- a/theories/Reals/RList.v +++ b/theories/Reals/RList.v @@ -10,7 +10,7 @@ Require Rbase. Require Rfunctions. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Inductive Rlist : Type := | nil : Rlist diff --git a/theories/Reals/R_sqr.v b/theories/Reals/R_sqr.v index 2fa84607f..f710c5120 100644 --- a/theories/Reals/R_sqr.v +++ b/theories/Reals/R_sqr.v @@ -10,7 +10,7 @@ Require Rbase. Require Rbasic_fun. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (****************************************************) (* Rsqr : some results *) diff --git a/theories/Reals/R_sqrt.v b/theories/Reals/R_sqrt.v index 0fd419288..c3997a312 100644 --- a/theories/Reals/R_sqrt.v +++ b/theories/Reals/R_sqrt.v @@ -11,7 +11,7 @@ Require Rbase. Require Rfunctions. Require Rsqrt_def. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (* Here is a continuous extension of Rsqrt on R *) Definition sqrt : R->R := [x:R](Cases (case_Rabsolu x) of diff --git a/theories/Reals/Ranalysis.v b/theories/Reals/Ranalysis.v index d467261c7..6e144928e 100644 --- a/theories/Reals/Ranalysis.v +++ b/theories/Reals/Ranalysis.v @@ -28,7 +28,7 @@ Require Export RList. Require Export Sqrt_reg. Require Export Ranalysis4. Require Export Rpower. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Axiom AppVar : R. diff --git a/theories/Reals/Ranalysis1.v b/theories/Reals/Ranalysis1.v index 2b883f7b6..aa41a8ae0 100644 --- a/theories/Reals/Ranalysis1.v +++ b/theories/Reals/Ranalysis1.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Export Rlimit. Require Export Rderiv. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Implicit Variable Type f:R->R. (****************************************************) diff --git a/theories/Reals/Ranalysis2.v b/theories/Reals/Ranalysis2.v index 05cfabcba..d13e96668 100644 --- a/theories/Reals/Ranalysis2.v +++ b/theories/Reals/Ranalysis2.v @@ -11,7 +11,7 @@ Require Rbase. Require Rfunctions. Require Ranalysis1. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Lemma formule : (x,h,l1,l2:R;f1,f2:R->R) ``h<>0`` -> ``(f2 x)<>0`` -> ``(f2 (x+h))<>0`` -> ``((f1 (x+h))/(f2 (x+h))-(f1 x)/(f2 x))/h-(l1*(f2 x)-l2*(f1 x))/(Rsqr (f2 x))`` == ``/(f2 (x+h))*(((f1 (x+h))-(f1 x))/h-l1) + l1/((f2 x)*(f2 (x+h)))*((f2 x)-(f2 (x+h))) - (f1 x)/((f2 x)*(f2 (x+h)))*(((f2 (x+h))-(f2 x))/h-l2) + (l2*(f1 x))/((Rsqr (f2 x))*(f2 (x+h)))*((f2 (x+h))-(f2 x))``. diff --git a/theories/Reals/Ranalysis3.v b/theories/Reals/Ranalysis3.v index 35f28aa64..7137deac3 100644 --- a/theories/Reals/Ranalysis3.v +++ b/theories/Reals/Ranalysis3.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Ranalysis1. Require Ranalysis2. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (* Division *) Theorem derivable_pt_lim_div : (f1,f2:R->R;x,l1,l2:R) (derivable_pt_lim f1 x l1) -> (derivable_pt_lim f2 x l2) -> ~``(f2 x)==0``-> (derivable_pt_lim (div_fct f1 f2) x ``(l1*(f2 x)-l2*(f1 x))/(Rsqr (f2 x))``). diff --git a/theories/Reals/Ranalysis4.v b/theories/Reals/Ranalysis4.v index 23c52c330..4da04bab8 100644 --- a/theories/Reals/Ranalysis4.v +++ b/theories/Reals/Ranalysis4.v @@ -15,7 +15,7 @@ Require Rtrigo. Require Ranalysis1. Require Ranalysis3. Require Exp_prop. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Lemma derivable_pt_inv : (f:R->R;x:R) ``(f x)<>0`` -> (derivable_pt f x) -> (derivable_pt (inv_fct f) x). diff --git a/theories/Reals/Raxioms.v b/theories/Reals/Raxioms.v index 6775958fc..3d312634d 100644 --- a/theories/Reals/Raxioms.v +++ b/theories/Reals/Raxioms.v @@ -15,7 +15,7 @@ Require Export ZArith_base. Require Export Rsyntax. Require Export TypeSyntax. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*********************************************************) (* Field axioms *) diff --git a/theories/Reals/Rbasic_fun.v b/theories/Reals/Rbasic_fun.v index 0c173c951..71fa79ad2 100644 --- a/theories/Reals/Rbasic_fun.v +++ b/theories/Reals/Rbasic_fun.v @@ -16,7 +16,7 @@ Require Rbase. Require R_Ifp. Require Fourier. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Implicit Variable Type r:R. diff --git a/theories/Reals/Rcomplete.v b/theories/Reals/Rcomplete.v index e62db41e5..c9f2596aa 100644 --- a/theories/Reals/Rcomplete.v +++ b/theories/Reals/Rcomplete.v @@ -13,7 +13,7 @@ Require Rfunctions. Require Rseries. Require SeqProp. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (****************************************************) (* R is complete : *) diff --git a/theories/Reals/Rderiv.v b/theories/Reals/Rderiv.v index 392c299a0..d73c10168 100644 --- a/theories/Reals/Rderiv.v +++ b/theories/Reals/Rderiv.v @@ -20,7 +20,7 @@ Require Fourier. Require Classical_Prop. Require Classical_Pred_Type. Require Omega. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*********) Definition D_x:(R->Prop)->R->R->Prop:=[D:R->Prop][y:R][x:R] diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 1131f1167..b7be1f077 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -25,7 +25,7 @@ Require Export SplitRmult. Require Export ArithProp. Require Omega. Require Zpower. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*******************************) (** Factorial *) diff --git a/theories/Reals/Rgeom.v b/theories/Reals/Rgeom.v index 831b32b9e..8168571e8 100644 --- a/theories/Reals/Rgeom.v +++ b/theories/Reals/Rgeom.v @@ -13,7 +13,7 @@ Require Rfunctions. Require SeqSeries. Require Rtrigo. Require R_sqrt. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition dist_euc [x0,y0,x1,y1:R] : R := ``(sqrt ((Rsqr (x0-x1))+(Rsqr (y0-y1))))``. diff --git a/theories/Reals/RiemannInt.v b/theories/Reals/RiemannInt.v index 55869a110..63322838a 100644 --- a/theories/Reals/RiemannInt.v +++ b/theories/Reals/RiemannInt.v @@ -16,7 +16,7 @@ Require RiemannInt_SF. Require Classical_Prop. Require Classical_Pred_Type. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Implicit Arguments On. diff --git a/theories/Reals/RiemannInt_SF.v b/theories/Reals/RiemannInt_SF.v index 46157e3c9..d436e780f 100644 --- a/theories/Reals/RiemannInt_SF.v +++ b/theories/Reals/RiemannInt_SF.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Ranalysis. Require Classical_Prop. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Implicit Arguments On. diff --git a/theories/Reals/Rlimit.v b/theories/Reals/Rlimit.v index 7f2baa8ef..f21ddcef9 100644 --- a/theories/Reals/Rlimit.v +++ b/theories/Reals/Rlimit.v @@ -17,7 +17,7 @@ Require Rbase. Require Rfunctions. Require Classical_Prop. Require Fourier. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*******************************) (* Calculus *) diff --git a/theories/Reals/Rpower.v b/theories/Reals/Rpower.v index e76236a89..0c641c692 100644 --- a/theories/Reals/Rpower.v +++ b/theories/Reals/Rpower.v @@ -23,7 +23,7 @@ Require Rsqrt_def. Require R_sqrt. Require MVT. Require Ranalysis4. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma P_Rmin: (P : R -> Prop) (x, y : R) (P x) -> (P y) -> (P (Rmin x y)). Intros P x y H1 H2; Unfold Rmin; Case (total_order_Rle x y); Intro; Assumption. diff --git a/theories/Reals/Rprod.v b/theories/Reals/Rprod.v index 24eba0cef..10dd8eb83 100644 --- a/theories/Reals/Rprod.v +++ b/theories/Reals/Rprod.v @@ -14,7 +14,7 @@ Require Rfunctions. Require Rseries. Require PartSum. Require Binomial. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (* TT Ak; 1<=k<=N *) Fixpoint prod_f_SO [An:nat->R;N:nat] : R := Cases N of diff --git a/theories/Reals/Rsigma.v b/theories/Reals/Rsigma.v index 4769c0cd2..f0cefb2e8 100644 --- a/theories/Reals/Rsigma.v +++ b/theories/Reals/Rsigma.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Rseries. Require PartSum. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Set Implicit Arguments. diff --git a/theories/Reals/Rsqrt_def.v b/theories/Reals/Rsqrt_def.v index 8267692a6..2f11d3001 100644 --- a/theories/Reals/Rsqrt_def.v +++ b/theories/Reals/Rsqrt_def.v @@ -13,7 +13,7 @@ Require Rbase. Require Rfunctions. Require SeqSeries. Require Ranalysis1. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Fixpoint Dichotomy_lb [x,y:R;P:R->bool;N:nat] : R := Cases N of diff --git a/theories/Reals/Rtopology.v b/theories/Reals/Rtopology.v index 5dc510c66..c32e76ce2 100644 --- a/theories/Reals/Rtopology.v +++ b/theories/Reals/Rtopology.v @@ -14,7 +14,7 @@ Require Ranalysis1. Require RList. Require Classical_Prop. Require Classical_Pred_Type. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition included [D1,D2:R->Prop] : Prop := (x:R)(D1 x)->(D2 x). Definition disc [x:R;delta:posreal] : R->Prop := [y:R]``(Rabsolu (y-x))<delta``. diff --git a/theories/Reals/Rtrigo.v b/theories/Reals/Rtrigo.v index 28a9fccb8..c2fbf5d32 100644 --- a/theories/Reals/Rtrigo.v +++ b/theories/Reals/Rtrigo.v @@ -19,7 +19,7 @@ Require Export Cos_plus. Require ZArith_base. Require Zcomplements. Require Classical_Prop. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (** sin_PI2 is the only remaining axiom **) Axiom sin_PI2 : ``(sin (PI/2))==1``. diff --git a/theories/Reals/Rtrigo_alt.v b/theories/Reals/Rtrigo_alt.v index 1f8b0ad07..87dbc98b4 100644 --- a/theories/Reals/Rtrigo_alt.v +++ b/theories/Reals/Rtrigo_alt.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require SeqSeries. Require Rtrigo_def. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*****************************************************************) (* Using series definitions of cos and sin *) diff --git a/theories/Reals/Rtrigo_calc.v b/theories/Reals/Rtrigo_calc.v index 925d7be95..52a1fa030 100644 --- a/theories/Reals/Rtrigo_calc.v +++ b/theories/Reals/Rtrigo_calc.v @@ -13,7 +13,7 @@ Require Rfunctions. Require SeqSeries. Require Rtrigo. Require R_sqrt. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma tan_PI : ``(tan PI)==0``. Unfold tan; Rewrite sin_PI; Rewrite cos_PI; Unfold Rdiv; Apply Rmult_Ol. diff --git a/theories/Reals/Rtrigo_def.v b/theories/Reals/Rtrigo_def.v index 8ede5a7a1..a2b2ebe05 100644 --- a/theories/Reals/Rtrigo_def.v +++ b/theories/Reals/Rtrigo_def.v @@ -13,7 +13,7 @@ Require Rfunctions. Require SeqSeries. Require Rtrigo_fun. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (*****************************) (* Definition of exponential *) diff --git a/theories/Reals/Rtrigo_reg.v b/theories/Reals/Rtrigo_reg.v index 6ec18e56a..bc04d7470 100644 --- a/theories/Reals/Rtrigo_reg.v +++ b/theories/Reals/Rtrigo_reg.v @@ -14,7 +14,7 @@ Require SeqSeries. Require Rtrigo. Require Ranalysis1. Require PSeries_reg. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Lemma CVN_R_cos : (fn:nat->R->R) (fn == [N:nat][x:R]``(pow (-1) N)/(INR (fact (mult (S (S O)) N)))*(pow x (mult (S (S O)) N))``) -> (CVN_R fn). Unfold CVN_R; Intros. diff --git a/theories/Reals/SeqProp.v b/theories/Reals/SeqProp.v index 3f1a84f9d..a49727b87 100644 --- a/theories/Reals/SeqProp.v +++ b/theories/Reals/SeqProp.v @@ -13,7 +13,7 @@ Require Rfunctions. Require Rseries. Require Classical. Require Max. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. Definition Un_decreasing [Un:nat->R] : Prop := (n:nat) (Rle (Un (S n)) (Un n)). Definition opp_seq [Un:nat->R] : nat->R := [n:nat]``-(Un n)``. diff --git a/theories/Reals/SeqSeries.v b/theories/Reals/SeqSeries.v index f3cc24ae9..d968112c5 100644 --- a/theories/Reals/SeqSeries.v +++ b/theories/Reals/SeqSeries.v @@ -21,7 +21,7 @@ Require Export Rsigma. Require Export Rprod. Require Export Cauchy_prod. Require Export Alembert. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Lemma sum_maj1 : (fn:nat->R->R;An:nat->R;x,l1,l2:R;N:nat) (Un_cv [n:nat](SP fn n x) l1) -> (Un_cv [n:nat](sum_f_R0 An n) l2) -> ((n:nat)``(Rabsolu (fn n x))<=(An n)``) -> ``(Rabsolu (l1-(SP fn N x)))<=l2-(sum_f_R0 An N)``. diff --git a/theories/Reals/Sqrt_reg.v b/theories/Reals/Sqrt_reg.v index 7d282e592..859c95753 100644 --- a/theories/Reals/Sqrt_reg.v +++ b/theories/Reals/Sqrt_reg.v @@ -12,7 +12,7 @@ Require Rbase. Require Rfunctions. Require Ranalysis1. Require R_sqrt. -V7only [Import R_scope.]. +V7only [Import R_scope.]. Open Scope R_scope. (**********) Lemma sqrt_var_maj : (h:R) ``(Rabsolu h) <= 1`` -> ``(Rabsolu ((sqrt (1+h))-1))<=(Rabsolu h)``. |