Commit c429778c by Guillaume Melquiond

### Added some Rabs versions of rewriting lemmas.

parent 7b301bb5
 ... ... @@ -1378,6 +1378,18 @@ apply ln_beta_unique. now rewrite Rabs_Ropp. Qed. Theorem ln_beta_abs : forall x, projT1 (ln_beta (Rabs x)) = projT1 (ln_beta x). Proof. intros x. set (m := projT1 (ln_beta x)). unfold Rabs. case Rcase_abs ; intros _. now rewrite ln_beta_opp. apply refl_equal. Qed. Theorem ln_beta_monotone_abs : forall x y, (x <> 0)%R -> (Rabs x <= Rabs y)%R -> ... ...
 ... ... @@ -82,6 +82,15 @@ now rewrite 2!Zfloor_Z2R. Qed. *) Theorem canonic_exponent_abs : forall x, canonic_exponent (Rabs x) = canonic_exponent x. Proof. intros x. unfold canonic_exponent. now rewrite ln_beta_abs. Qed. Theorem generic_format_bpow : forall e, (fexp (e + 1) <= e)%Z -> generic_format (bpow e). ... ...
 ... ... @@ -18,6 +18,22 @@ Definition ulp x := bpow (canonic_exponent beta fexp x). Definition F := generic_format beta fexp. Theorem ulp_opp : forall x, ulp (- x) = ulp x. Proof. intros x. unfold ulp. now rewrite canonic_exponent_opp. Qed. Theorem ulp_abs : forall x, ulp (Rabs x) = ulp x. Proof. intros x. unfold ulp. now rewrite canonic_exponent_abs. Qed. Theorem ulp_DN_UP : forall x, ~ F x -> rounding beta fexp ZrndUP x = (rounding beta fexp ZrndDN x + ulp x)%R. ... ...
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