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-rw-r--r--theories/Reals/Ranalysis_reg.v109
1 files changed, 59 insertions, 50 deletions
diff --git a/theories/Reals/Ranalysis_reg.v b/theories/Reals/Ranalysis_reg.v
index 2465f039..0c27d407 100644
--- a/theories/Reals/Ranalysis_reg.v
+++ b/theories/Reals/Ranalysis_reg.v
@@ -35,7 +35,7 @@ Qed.
(**********)
Ltac intro_hyp_glob trm :=
- match constr:trm with
+ match constr:(trm) with
| (?X1 + ?X2)%F =>
match goal with
| |- (derivable _) => intro_hyp_glob X1; intro_hyp_glob X2
@@ -55,7 +55,7 @@ Ltac intro_hyp_glob trm :=
| _ => idtac
end
| (?X1 / ?X2)%F =>
- let aux := constr:X2 in
+ let aux := constr:(X2) in
match goal with
| _:(forall x0:R, aux x0 <> 0) |- (derivable _) =>
intro_hyp_glob X1; intro_hyp_glob X2
@@ -82,7 +82,7 @@ Ltac intro_hyp_glob trm :=
| _ => idtac
end
| (/ ?X1)%F =>
- let aux := constr:X1 in
+ let aux := constr:(X1) in
match goal with
| _:(forall x0:R, aux x0 <> 0) |- (derivable _) =>
intro_hyp_glob X1
@@ -108,7 +108,8 @@ Ltac intro_hyp_glob trm :=
| (pow_fct _) => idtac
| Rabs => idtac
| ?X1 =>
- let p := constr:X1 in
+ let p := constr:(X1) in
+ let HYPPD := fresh "HYPPD" in
match goal with
| _:(derivable p) |- _ => idtac
| |- (derivable p) => idtac
@@ -130,7 +131,7 @@ Ltac intro_hyp_glob trm :=
(**********)
Ltac intro_hyp_pt trm pt :=
- match constr:trm with
+ match constr:(trm) with
| (?X1 + ?X2)%F =>
match goal with
| |- (derivable_pt _ _) => intro_hyp_pt X1 pt; intro_hyp_pt X2 pt
@@ -156,7 +157,7 @@ Ltac intro_hyp_pt trm pt :=
| _ => idtac
end
| (?X1 / ?X2)%F =>
- let aux := constr:X2 in
+ let aux := constr:(X2) in
match goal with
| _:(aux pt <> 0) |- (derivable_pt _ _) =>
intro_hyp_pt X1 pt; intro_hyp_pt X2 pt
@@ -202,7 +203,7 @@ Ltac intro_hyp_pt trm pt :=
| _ => idtac
end
| (/ ?X1)%F =>
- let aux := constr:X1 in
+ let aux := constr:(X1) in
match goal with
| _:(aux pt <> 0) |- (derivable_pt _ _) =>
intro_hyp_pt X1 pt
@@ -249,7 +250,8 @@ Ltac intro_hyp_pt trm pt :=
| _ => idtac
end
| ?X1 =>
- let p := constr:X1 in
+ let p := constr:(X1) in
+ let HYPPD := fresh "HYPPD" in
match goal with
| _:(derivable_pt p pt) |- _ => idtac
| |- (derivable_pt p pt) => idtac
@@ -341,8 +343,10 @@ Ltac is_diff_pt :=
| _:(derivable_pt ?X1 ?X2) |- (derivable_pt ?X1 ?X2) =>
assumption
| _:(derivable ?X1) |- (derivable_pt ?X1 ?X2) =>
+ let HypDDPT := fresh "HypDDPT" in
cut (derivable X1); [ intro HypDDPT; apply HypDDPT | assumption ]
| |- (True -> derivable_pt _ _) =>
+ let HypTruE := fresh "HypTruE" in
intro HypTruE; clear HypTruE; is_diff_pt
| _ =>
try
@@ -411,6 +415,7 @@ Ltac is_diff_glob :=
apply (derivable_comp X2 X1); is_diff_glob
| _:(derivable ?X1) |- (derivable ?X1) => assumption
| |- (True -> derivable _) =>
+ let HypTruE := fresh "HypTruE" in
intro HypTruE; clear HypTruE; is_diff_glob
| _ =>
try
@@ -490,14 +495,17 @@ Ltac is_cont_pt :=
| _:(continuity_pt ?X1 ?X2) |- (continuity_pt ?X1 ?X2) =>
assumption
| _:(continuity ?X1) |- (continuity_pt ?X1 ?X2) =>
+ let HypDDPT := fresh "HypDDPT" in
cut (continuity X1); [ intro HypDDPT; apply HypDDPT | assumption ]
| _:(derivable_pt ?X1 ?X2) |- (continuity_pt ?X1 ?X2) =>
apply derivable_continuous_pt; assumption
| _:(derivable ?X1) |- (continuity_pt ?X1 ?X2) =>
+ let HypDDPT := fresh "HypDDPT" in
cut (continuity X1);
[ intro HypDDPT; apply HypDDPT
| apply derivable_continuous; assumption ]
| |- (True -> continuity_pt _ _) =>
+ let HypTruE := fresh "HypTruE" in
intro HypTruE; clear HypTruE; is_cont_pt
| _ =>
try
@@ -567,6 +575,7 @@ Ltac is_cont_glob :=
apply (continuity_comp X2 X1); try is_cont_glob || assumption
| _:(continuity ?X1) |- (continuity ?X1) => assumption
| |- (True -> continuity _) =>
+ let HypTruE := fresh "HypTruE" in
intro HypTruE; clear HypTruE; is_cont_glob
| _:(derivable ?X1) |- (continuity ?X1) =>
apply derivable_continuous; assumption
@@ -578,89 +587,89 @@ Ltac is_cont_glob :=
(**********)
Ltac rew_term trm :=
- match constr:trm with
+ match constr:(trm) with
| (?X1 + ?X2) =>
let p1 := rew_term X1 with p2 := rew_term X2 in
- match constr:p1 with
+ match constr:(p1) with
| (fct_cte ?X3) =>
- match constr:p2 with
+ match constr:(p2) with
| (fct_cte ?X4) => constr:(fct_cte (X3 + X4))
- | _ => constr:(p1 + p2)%F
+ | _ => constr:((p1 + p2)%F)
end
- | _ => constr:(p1 + p2)%F
+ | _ => constr:((p1 + p2)%F)
end
| (?X1 - ?X2) =>
let p1 := rew_term X1 with p2 := rew_term X2 in
- match constr:p1 with
+ match constr:(p1) with
| (fct_cte ?X3) =>
- match constr:p2 with
+ match constr:(p2) with
| (fct_cte ?X4) => constr:(fct_cte (X3 - X4))
- | _ => constr:(p1 - p2)%F
+ | _ => constr:((p1 - p2)%F)
end
- | _ => constr:(p1 - p2)%F
+ | _ => constr:((p1 - p2)%F)
end
| (?X1 / ?X2) =>
let p1 := rew_term X1 with p2 := rew_term X2 in
- match constr:p1 with
+ match constr:(p1) with
| (fct_cte ?X3) =>
- match constr:p2 with
+ match constr:(p2) with
| (fct_cte ?X4) => constr:(fct_cte (X3 / X4))
- | _ => constr:(p1 / p2)%F
+ | _ => constr:((p1 / p2)%F)
end
| _ =>
- match constr:p2 with
- | (fct_cte ?X4) => constr:(p1 * fct_cte (/ X4))%F
- | _ => constr:(p1 / p2)%F
+ match constr:(p2) with
+ | (fct_cte ?X4) => constr:((p1 * fct_cte (/ X4))%F)
+ | _ => constr:((p1 / p2)%F)
end
end
| (?X1 * / ?X2) =>
let p1 := rew_term X1 with p2 := rew_term X2 in
- match constr:p1 with
+ match constr:(p1) with
| (fct_cte ?X3) =>
- match constr:p2 with
+ match constr:(p2) with
| (fct_cte ?X4) => constr:(fct_cte (X3 / X4))
- | _ => constr:(p1 / p2)%F
+ | _ => constr:((p1 / p2)%F)
end
| _ =>
- match constr:p2 with
- | (fct_cte ?X4) => constr:(p1 * fct_cte (/ X4))%F
- | _ => constr:(p1 / p2)%F
+ match constr:(p2) with
+ | (fct_cte ?X4) => constr:((p1 * fct_cte (/ X4))%F)
+ | _ => constr:((p1 / p2)%F)
end
end
| (?X1 * ?X2) =>
let p1 := rew_term X1 with p2 := rew_term X2 in
- match constr:p1 with
+ match constr:(p1) with
| (fct_cte ?X3) =>
- match constr:p2 with
+ match constr:(p2) with
| (fct_cte ?X4) => constr:(fct_cte (X3 * X4))
- | _ => constr:(p1 * p2)%F
+ | _ => constr:((p1 * p2)%F)
end
- | _ => constr:(p1 * p2)%F
+ | _ => constr:((p1 * p2)%F)
end
| (- ?X1) =>
let p := rew_term X1 in
- match constr:p with
+ match constr:(p) with
| (fct_cte ?X2) => constr:(fct_cte (- X2))
- | _ => constr:(- p)%F
+ | _ => constr:((- p)%F)
end
| (/ ?X1) =>
let p := rew_term X1 in
- match constr:p with
+ match constr:(p) with
| (fct_cte ?X2) => constr:(fct_cte (/ X2))
- | _ => constr:(/ p)%F
+ | _ => constr:((/ p)%F)
end
- | (?X1 AppVar) => constr:X1
+ | (?X1 AppVar) => constr:(X1)
| (?X1 ?X2) =>
let p := rew_term X2 in
- match constr:p with
+ match constr:(p) with
| (fct_cte ?X3) => constr:(fct_cte (X1 X3))
| _ => constr:(comp X1 p)
end
- | AppVar => constr:id
+ | AppVar => constr:(id)
| (AppVar ^ ?X1) => constr:(pow_fct X1)
| (?X1 ^ ?X2) =>
let p := rew_term X1 in
- match constr:p with
+ match constr:(p) with
| (fct_cte ?X3) => constr:(fct_cte (pow_fct X2 X3))
| _ => constr:(comp (pow_fct X2) p)
end
@@ -669,7 +678,7 @@ Ltac rew_term trm :=
(**********)
Ltac deriv_proof trm pt :=
- match constr:trm with
+ match constr:(trm) with
| (?X1 + ?X2)%F =>
let p1 := deriv_proof X1 pt with p2 := deriv_proof X2 pt in
constr:(derivable_pt_plus X1 X2 pt p1 p2)
@@ -684,14 +693,14 @@ Ltac deriv_proof trm pt :=
| id:(?X2 pt <> 0) |- _ =>
let p1 := deriv_proof X1 pt with p2 := deriv_proof X2 pt in
constr:(derivable_pt_div X1 X2 pt p1 p2 id)
- | _ => constr:False
+ | _ => constr:(False)
end
| (/ ?X1)%F =>
match goal with
| id:(?X1 pt <> 0) |- _ =>
let p1 := deriv_proof X1 pt in
constr:(derivable_pt_inv X1 pt p1 id)
- | _ => constr:False
+ | _ => constr:(False)
end
| (comp ?X1 ?X2) =>
let pt_f1 := eval cbv beta in (X2 pt) in
@@ -710,21 +719,21 @@ Ltac deriv_proof trm pt :=
| sqrt =>
match goal with
| id:(0 < pt) |- _ => constr:(derivable_pt_sqrt pt id)
- | _ => constr:False
+ | _ => constr:(False)
end
| (fct_cte ?X1) => constr:(derivable_pt_const X1 pt)
| ?X1 =>
- let aux := constr:X1 in
+ let aux := constr:(X1) in
match goal with
- | id:(derivable_pt aux pt) |- _ => constr:id
+ | id:(derivable_pt aux pt) |- _ => constr:(id)
| id:(derivable aux) |- _ => constr:(id pt)
- | _ => constr:False
+ | _ => constr:(False)
end
end.
(**********)
Ltac simplify_derive trm pt :=
- match constr:trm with
+ match constr:(trm) with
| (?X1 + ?X2)%F =>
try rewrite derive_pt_plus; simplify_derive X1 pt;
simplify_derive X2 pt
@@ -753,7 +762,7 @@ Ltac simplify_derive trm pt :=
| Rsqr => try rewrite derive_pt_Rsqr
| sqrt => try rewrite derive_pt_sqrt
| ?X1 =>
- let aux := constr:X1 in
+ let aux := constr:(X1) in
match goal with
| id:(derive_pt aux pt ?X2 = _),H:(derivable aux) |- _ =>
try replace (derive_pt aux pt (H pt)) with (derive_pt aux pt X2);
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-06 06:37:43 +0000