diff options
author | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-28 16:54:39 +0000 |
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committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-28 16:54:39 +0000 |
commit | 8afe5c8aebeb13ad0e41f2a5c39c9b03a787641a (patch) | |
tree | 32494c7edff9608b2760722bbb5ccf46f5e592af /test-suite | |
parent | 5816479511c4702d9e7159a9045718565bb62545 (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.v | 52 |
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. |