Commit c1874b2d by Guillaume Melquiond

### Factored proofs.

parent f3c15581
 ... ... @@ -386,6 +386,15 @@ Section Fprop_relative_FLT. Variable emin prec : Z. Variable Hp : Zlt 0 prec. Lemma relative_error_FLT_aux : forall k, (emin + prec - 1 < k)%Z -> (prec <= k - FLT_exp emin prec k)%Z. Proof. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. Qed. Variable rnd : Zround. Theorem relative_error_FLT_F2R : ... ... @@ -396,10 +405,7 @@ Proof. intros m x Hx. apply generic_relative_error_F2R. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. exact Hx. Qed. ... ... @@ -411,10 +417,7 @@ Proof. intros x Hx. apply generic_relative_error with (emin + prec - 1)%Z. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. exact Hx. Qed. ... ... @@ -453,10 +456,7 @@ Proof. intros x Hx. apply generic_relative_error_N with (emin + prec - 1)%Z. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. exact Hx. Qed. ... ... @@ -485,10 +485,7 @@ Proof. intros x Hx. apply generic_relative_error_N_2 with (emin + prec - 1)%Z. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. exact Hp. exact Hx. Qed. ... ... @@ -500,10 +497,7 @@ Proof. intros m x. apply generic_relative_error_N_F2R. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. Qed. Theorem relative_error_N_FLT_F2R_ex : ... ... @@ -528,10 +522,7 @@ Proof. intros m x. apply generic_relative_error_N_F2R_2. now apply FLT_exp_correct. intros k Hk. unfold FLT_exp. generalize (Zmax_spec (k - prec) emin). omega. apply relative_error_FLT_aux. exact Hp. Qed. ... ... @@ -594,6 +585,14 @@ Section Fprop_relative_FLX. Variable prec : Z. Variable Hp : Zlt 0 prec. Lemma relative_error_FLX_aux : forall k, (prec <= k - FLX_exp prec k)%Z. Proof. intros k. unfold FLX_exp. omega. Qed. Variable rnd : Zround. Theorem relative_error_FLX : ... ... @@ -607,8 +606,7 @@ specialize (He Hx). apply generic_relative_error with (ex - 1)%Z. now apply FLX_exp_correct. intros k _. unfold FLX_exp. omega. apply relative_error_FLX_aux. apply He. Qed. ... ... @@ -636,8 +634,7 @@ specialize (He Hx). apply generic_relative_error_2 with (ex - 1)%Z. now apply FLX_exp_correct. intros k _. unfold FLX_exp. omega. apply relative_error_FLX_aux. exact Hp. apply He. Qed. ... ... @@ -662,8 +659,7 @@ specialize (He Hx). apply generic_relative_error_N with (ex - 1)%Z. now apply FLX_exp_correct. intros k _. unfold FLX_exp. omega. apply relative_error_FLX_aux. apply He. Qed. ... ... @@ -701,8 +697,7 @@ specialize (He Hx). apply generic_relative_error_N_2 with (ex - 1)%Z. now apply FLX_exp_correct. intros k _. unfold FLX_exp. omega. apply relative_error_FLX_aux. exact Hp. apply He. Qed. ... ...
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