diff options
Diffstat (limited to 'theories/Reals/Rfunctions.v')
| -rw-r--r-- | theories/Reals/Rfunctions.v | 13 |
1 files changed, 13 insertions, 0 deletions
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 9beee06c5..6e9a34ab4 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -520,6 +520,12 @@ Proof. apply Rle_trans with (Rabs y); [ apply Rabs_pos | exact H ]. Qed. +Lemma Rsqr_pow2 : forall x, Rsqr x = x ^ 2. +Proof. +intros; unfold Rsqr; simpl; rewrite Rmult_1_r; reflexivity. +Qed. + + (*******************************) (** * PowerRZ *) (*******************************) @@ -783,6 +789,13 @@ Proof. ring. Qed. +Lemma R_dist_mult_l : forall a b c, + R_dist (a * b) (a * c) = Rabs a * R_dist b c. +Proof. +unfold R_dist. +intros a b c; rewrite <- Rmult_minus_distr_l, Rabs_mult; reflexivity. +Qed. + (*******************************) (** * Infinite Sum *) (*******************************) |