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authorGravatar desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-01-28 16:54:39 +0000
committerGravatar desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-01-28 16:54:39 +0000
commit8afe5c8aebeb13ad0e41f2a5c39c9b03a787641a (patch)
tree32494c7edff9608b2760722bbb5ccf46f5e592af /test-suite
parent5816479511c4702d9e7159a9045718565bb62545 (diff)
MAJ pour Reg
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3615 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'test-suite')
-rw-r--r--test-suite/success/Reg.v52
1 files changed, 26 insertions, 26 deletions
diff --git a/test-suite/success/Reg.v b/test-suite/success/Reg.v
index b088321d3..eaa0690cb 100644
--- a/test-suite/success/Reg.v
+++ b/test-suite/success/Reg.v
@@ -8,129 +8,129 @@ Axiom dy_0 : (derive_pt y R0 (d_y R0)) == R1.
Lemma essai0 : (continuity_pt [x:R]``(x+2)/(y x)+x/(y x)`` R0).
Assert H := d_y.
Assert H0 := n_y.
-Reg().
+Reg.
Qed.
Lemma essai1 : (derivable_pt [x:R]``/2*(sin x)`` ``1``).
-Reg ().
+Reg.
Qed.
Lemma essai2 : (continuity [x:R]``(Rsqr x)*(cos (x*x))+x``).
-Reg ().
+Reg.
Qed.
Lemma essai3 : (derivable_pt [x:R]``x*((Rsqr x)+3)`` R0).
-Reg ().
+Reg.
Qed.
Lemma essai4 : (derivable [x:R]``(x+x)*(sin x)``).
-Reg ().
+Reg.
Qed.
Lemma essai5 : (derivable [x:R]``1+(sin (2*x+3))*(cos (cos x))``).
-Reg ().
+Reg.
Qed.
Lemma essai6 : (derivable [x:R]``(cos (x+3))``).
-Reg ().
+Reg.
Qed.
Lemma essai7 : (derivable_pt [x:R]``(cos (/(sqrt x)))*(Rsqr ((sin x)+1))`` R1).
-Reg ().
+Reg.
Apply Rlt_R0_R1.
Red; Intro; Rewrite sqrt_1 in H; Assert H0 := R1_neq_R0; Elim H0; Assumption.
Qed.
Lemma essai8 : (derivable_pt [x:R]``(sqrt ((Rsqr x)+(sin x)+1))`` R0).
-Reg ().
+Reg.
Rewrite sin_0.
Rewrite Rsqr_O.
Replace ``0+0+1`` with ``1``; [Apply Rlt_R0_R1 | Ring].
Qed.
Lemma essai9 : (derivable_pt (plus_fct id sin) R1).
-Reg ().
+Reg.
Qed.
Lemma essai10 : (derivable_pt [x:R]``x+2`` R0).
-Reg().
+Reg.
Qed.
Lemma essai11 : (derive_pt [x:R]``x+2`` R0 essai10)==R1.
-Reg().
+Reg.
Qed.
Lemma essai12 : (derivable [x:R]``x+(Rsqr (x+2))``).
-Reg().
+Reg.
Qed.
Lemma essai13 : (derive_pt [x:R]``x+(Rsqr (x+2))`` R0 (essai12 R0)) == ``5``.
-Reg().
+Reg.
Qed.
Lemma essai14 : (derivable_pt [x:R]``2*x+x`` ``2``).
-Reg ().
+Reg.
Qed.
Lemma essai15 : (derive_pt [x:R]``2*x+x`` ``2`` essai14) == ``3``.
-Reg().
+Reg.
Qed.
Lemma essai16 : (derivable_pt [x:R]``x+(sin x)`` R0).
-Reg().
+Reg.
Qed.
Lemma essai17 : (derive_pt [x:R]``x+(sin x)`` R0 essai16)==``2``.
-Reg ().
+Reg.
Rewrite cos_0.
Reflexivity.
Qed.
Lemma essai18 : (derivable_pt [x:R]``x+(y x)`` ``0``).
Assert H := d_y.
-Reg ().
+Reg.
Qed.
Lemma essai19 : (derive_pt [x:R]``x+(y x)`` ``0`` essai18) == ``2``.
Assert H := dy_0.
Assert H0 := d_y.
-Reg ().
+Reg.
Qed.
Axiom z:R->R.
Axiom d_z: (derivable z).
Lemma essai20 : (derivable_pt [x:R]``(z (y x))`` R0).
-Reg ().
+Reg.
Apply d_y.
Apply d_z.
Qed.
Lemma essai21 : (derive_pt [x:R]``(z (y x))`` R0 essai20) == R1.
Assert H := dy_0.
-Reg().
+Reg.
Abort.
Lemma essai22 : (derivable [x:R]``(sin (z x))+(Rsqr (z x))/(y x)``).
Assert H := d_y.
-Reg().
+Reg.
Apply n_y.
Apply d_z.
Qed.
(* Pour tester la continuite de sqrt en 0 *)
Lemma essai23 : (continuity_pt [x:R]``(sin (sqrt (x-1)))+(exp (Rsqr ((sqrt x)+3)))`` R1).
-Reg().
+Reg.
Left; Apply Rlt_R0_R1.
Right; Unfold Rminus; Rewrite Rplus_Ropp_r; Reflexivity.
Qed.
Lemma essai24 : (derivable [x:R]``(sqrt (x*x+2*x+2))+(Rabsolu (x*x+1))``).
-Reg ().
+Reg.
Replace ``x*x+2*x+2`` with ``(Rsqr (x+1))+1``.
Apply ge0_plus_gt0_is_gt0; [Apply pos_Rsqr | Apply Rlt_R0_R1].
Unfold Rsqr; Ring.
Red; Intro; Cut ``0<x*x+1``.
Intro; Rewrite H in H0; Elim (Rlt_antirefl ? H0).
Apply ge0_plus_gt0_is_gt0; [Replace ``x*x`` with (Rsqr x); [Apply pos_Rsqr | Reflexivity] | Apply Rlt_R0_R1].
-Qed. \ No newline at end of file
+Qed.