diff options
| author |  desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-21 16:20:51 +0000 |
|---|---|---|
| committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-21 16:20:51 +0000 |
| commit | d9a43db80ff4151406a0ed6e3b38c781a06ba8e7 (patch) | |
| tree | 7c123a3a53a6444d4454762e97461af54d3fa6ed /theories/Reals/Cos_plus.v | |
| parent | aa0ceff51bd696098c714f206e2e53a3d859a345 (diff) | |
Renommage dans Binomial.v
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3562 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Cos_plus.v')
| -rw-r--r-- | theories/Reals/Cos_plus.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Reals/Cos_plus.v b/theories/Reals/Cos_plus.v index d1c167c56..15f68c1bb 100644 --- a/theories/Reals/Cos_plus.v +++ b/theories/Reals/Cos_plus.v @@ -218,8 +218,8 @@ Apply Rlt_R0_R1. Unfold C; Apply RmaxLess1. Replace ``/(INR (mult (fact (mult (S (S O)) (S (plus n0 n)))) - (fact (mult (S (S O)) (minus N n0)))))`` with ``(Binome.C (mult (S (S O)) (S (plus N n))) (mult (S (S O)) (S (plus n0 n))))/(INR (fact (mult (S (S O)) (S (plus N n)))))``. -Apply Rle_trans with ``(Binome.C (mult (S (S O)) (S (plus N n))) (S (plus N n)))/(INR (fact (mult (S (S O)) (S (plus N n)))))``. + (fact (mult (S (S O)) (minus N n0)))))`` with ``(Binomial.C (mult (S (S O)) (S (plus N n))) (mult (S (S O)) (S (plus n0 n))))/(INR (fact (mult (S (S O)) (S (plus N n)))))``. +Apply Rle_trans with ``(Binomial.C (mult (S (S O)) (S (plus N n))) (S (plus N n)))/(INR (fact (mult (S (S O)) (S (plus N n)))))``. Unfold Rdiv; Do 2 Rewrite <- (Rmult_sym ``/(INR (fact (mult (S (S O)) (S (plus N n)))))``). Apply Rle_monotony. Left; Apply Rlt_Rinv; Apply INR_fact_lt_0. @@ -251,7 +251,7 @@ Assumption. Apply le_pred_n. Right. Unfold Rdiv; Rewrite Rmult_sym. -Unfold Binome.C. +Unfold Binomial.C. Unfold Rdiv; Repeat Rewrite <- Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1l. @@ -265,7 +265,7 @@ Rewrite mult_INR; Repeat Rewrite S_INR; Rewrite plus_INR; Ring. Apply le_n_2n. Apply INR_fact_neq_0. Unfold Rdiv; Rewrite Rmult_sym. -Unfold Binome.C. +Unfold Binomial.C. Unfold Rdiv; Repeat Rewrite <- Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1l. @@ -598,8 +598,8 @@ Apply Rlt_R0_R1. Unfold C; Apply RmaxLess1. Replace ``/(INR (mult (fact (plus (mult (S (S O)) (S (plus n0 n))) (S O))) - (fact (plus (mult (S (S O)) (minus N n0)) (S O)))))`` with ``(Binome.C (mult (S (S O)) (S (S (plus N n)))) (plus (mult (S (S O)) (S (plus n0 n))) (S O)))/(INR (fact (mult (S (S O)) (S (S (plus N n))))))``. -Apply Rle_trans with ``(Binome.C (mult (S (S O)) (S (S (plus N n)))) (S (S (plus N n))))/(INR (fact (mult (S (S O)) (S (S (plus N n))))))``. + (fact (plus (mult (S (S O)) (minus N n0)) (S O)))))`` with ``(Binomial.C (mult (S (S O)) (S (S (plus N n)))) (plus (mult (S (S O)) (S (plus n0 n))) (S O)))/(INR (fact (mult (S (S O)) (S (S (plus N n))))))``. +Apply Rle_trans with ``(Binomial.C (mult (S (S O)) (S (S (plus N n)))) (S (S (plus N n))))/(INR (fact (mult (S (S O)) (S (S (plus N n))))))``. Unfold Rdiv; Do 2 Rewrite <- (Rmult_sym ``/(INR (fact (mult (S (S O)) (S (S (plus N n))))))``). Apply Rle_monotony. Left; Apply Rlt_Rinv; Apply INR_fact_lt_0. @@ -635,7 +635,7 @@ Assumption. Apply le_pred_n. Right. Unfold Rdiv; Rewrite Rmult_sym. -Unfold Binome.C. +Unfold Binomial.C. Unfold Rdiv; Repeat Rewrite <- Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1l. @@ -649,7 +649,7 @@ Rewrite mult_INR; Repeat Rewrite S_INR; Rewrite plus_INR; Ring. Apply le_n_2n. Apply INR_fact_neq_0. Unfold Rdiv; Rewrite Rmult_sym. -Unfold Binome.C. +Unfold Binomial.C. Unfold Rdiv; Repeat Rewrite <- Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1l. |