diff options
Diffstat (limited to 'theories/Reals/R_sqr.v')
| -rw-r--r-- | theories/Reals/R_sqr.v | 31 |
1 files changed, 15 insertions, 16 deletions
diff --git a/theories/Reals/R_sqr.v b/theories/Reals/R_sqr.v index 2cd6e2fb9..8a711809e 100644 --- a/theories/Reals/R_sqr.v +++ b/theories/Reals/R_sqr.v @@ -168,6 +168,7 @@ Intros; Unfold Rsqr. Rewrite Rinv_Rmult; Try Reflexivity Orelse Assumption. Qed. +Import R_scope. Lemma canonical_Rsqr : (a:nonzeroreal;b,c,x:R) ``a*(Rsqr x)+b*x+c == a* (Rsqr (x+b/(2*a))) + (4*a*c - (Rsqr b))/(4*a)``. Intros. Rewrite Rsqr_plus. @@ -175,6 +176,7 @@ Repeat Rewrite Rmult_Rplus_distr. Repeat Rewrite Rplus_assoc. Apply Rplus_plus_r. Unfold Rdiv Rminus. +Replace ``2*1+2*1`` with ``4``; [Idtac | Ring]. Rewrite (Rmult_Rplus_distrl ``4*a*c`` ``-(Rsqr b)`` ``/(4*a)``). Rewrite Rsqr_times. Repeat Rewrite Rinv_Rmult. @@ -186,39 +188,36 @@ Rewrite (Rmult_sym ``2``). Repeat Rewrite Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1r. -Rewrite (Rmult_sym ``/4``). -Rewrite (Rmult_sym ``4``). +Rewrite (Rmult_sym ``/2``). +Rewrite (Rmult_sym ``2``). Repeat Rewrite Rmult_assoc; Rewrite <- Rinv_l_sym. Rewrite Rmult_1r. Rewrite (Rmult_sym a). -Rewrite Rmult_assoc. +Repeat Rewrite Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1r. -Rewrite (Rmult_sym x). +Rewrite (Rmult_sym ``2``). +Repeat Rewrite Rmult_assoc; Rewrite <- Rinv_l_sym. +Rewrite Rmult_1r. Repeat Rewrite Rplus_assoc. -Rewrite (Rplus_sym ``(Rsqr b)*((Rsqr (/2*/a))*a)``). +Rewrite (Rplus_sym ``(Rsqr b)*((Rsqr (/a*/2))*a)``). Repeat Rewrite Rplus_assoc. +Rewrite (Rmult_sym x). Apply Rplus_plus_r. -Rewrite Ropp_mul1. -Unfold Rsqr. -Repeat Rewrite Rmult_assoc. +Rewrite (Rmult_sym ``/a``). +Unfold Rsqr; Repeat Rewrite Rmult_assoc. Rewrite <- Rinv_l_sym. Rewrite Rmult_1r. -Rewrite <- (Rmult_sym ``(/a*/2)``). -Rewrite Rmult_assoc. -Rewrite <- (Rinv_Rmult ``2`` ``2``). -Replace ``2*2`` with ``4``. -Rewrite Rplus_Ropp_l. -Symmetry; Apply Rplus_Or. Ring. -DiscrR. -DiscrR. Apply (cond_nonzero a). +DiscrR. Apply (cond_nonzero a). DiscrR. DiscrR. Apply (cond_nonzero a). DiscrR. +DiscrR. +DiscrR. Apply (cond_nonzero a). DiscrR. Apply (cond_nonzero a). |