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author | 2002-05-31 21:04:33 +0000 | |
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committer | 2002-05-31 21:04:33 +0000 | |
commit | 6fe4d02936802bee35c73cdab2d08d8d4d3bd530 (patch) | |
tree | d31efd262284479b1bed93acf7869d7e77a95ccb /theories/Reals/Rbase.v | |
parent | f37224a45253f2ff98a2a0975fe3afe5c8b207a1 (diff) |
Ajout d'occurrences de Field (ne pas enlever)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2742 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Rbase.v')
-rw-r--r-- | theories/Reals/Rbase.v | 17 |
1 files changed, 4 insertions, 13 deletions
diff --git a/theories/Reals/Rbase.v b/theories/Reals/Rbase.v index d21fde297..069ebe3cd 100644 --- a/theories/Reals/Rbase.v +++ b/theories/Reals/Rbase.v @@ -531,8 +531,7 @@ Qed. (** Inverse *) Lemma Rinv_R1:``/1==1``. -Apply (r_Rmult_mult ``1`` ``/1`` ``1``); Auto with real. -Rewrite (Rinv_r R1 R1_neq_R0);Auto with real. +Field;Auto with real. Qed. Hints Resolve Rinv_R1 : real. @@ -545,26 +544,18 @@ Hints Resolve Rinv_neq_R0 : real. (*********) Lemma Rinv_Rinv:(r:R)``r<>0``->``/(/r)==r``. -Intros;Apply (r_Rmult_mult ``/r``); Auto with real. -Transitivity ``1``; Auto with real. +Intros;Field;Auto with real. Qed. Hints Resolve Rinv_Rinv : real. (*********) Lemma Rinv_Rmult:(r1,r2:R)``r1<>0``->``r2<>0``->``/(r1*r2)==(/r1)*(/r2)``. -Intros; Apply (r_Rmult_mult ``r1*r2``);Auto with real. -Transitivity ``1``; Auto with real. -Transitivity ``(r1*/r1)*(r2*(/r2))``; Auto with real. -Rewrite Rinv_r; Trivial. -Rewrite Rinv_r; Auto with real. -Ring. +Intros;Field;Auto with real. Qed. (*********) Lemma Ropp_Rinv:(r:R)``r<>0``->``-(/r)==/(-r)``. -Intros; Apply (r_Rmult_mult ``-r``);Auto with real. -Transitivity ``1``; Auto with real. -Rewrite (Ropp_mul2 r ``/r``); Auto with real. +Intros;Field;Auto with real. Qed. Lemma Rinv_r_simpl_r : (r1,r2:R)``r1<>0``->``r1*(/r1)*r2==r2``. |