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Commit 875447d5 by Guillaume Melquiond

### Removed useless theorems.

parent 84335f01
 ... ... @@ -191,44 +191,29 @@ rewrite <- opp_F2R. now apply f_equal. Qed. Theorem canonic_exponent_fexp_pos : Theorem canonic_exponent_fexp : forall x ex, (bpow (ex - 1) <= x < bpow ex)%R -> (bpow (ex - 1) <= Rabs x < bpow ex)%R -> canonic_exponent x = fexp ex. Proof. intros x ex Hx. unfold canonic_exponent. rewrite <- (Rabs_pos_eq x) in Hx. now rewrite ln_beta_unique with (1 := Hx). apply Rle_trans with (2 := proj1 Hx). apply bpow_ge_0. Qed. Theorem canonic_exponent_fexp_neg : Theorem canonic_exponent_fexp_pos : forall x ex, (bpow (ex - 1) <= -x < bpow ex)%R -> (bpow (ex - 1) <= x < bpow ex)%R -> canonic_exponent x = fexp ex. Proof. intros x ex Hx. unfold canonic_exponent. rewrite <- (Rabs_left1 x) in Hx. now rewrite ln_beta_unique with (1 := Hx). apply Ropp_le_cancel. rewrite Ropp_0. apply canonic_exponent_fexp. rewrite Rabs_pos_eq. exact Hx. apply Rle_trans with (2 := proj1 Hx). apply bpow_ge_0. Qed. Theorem canonic_exponent_fexp : forall x ex, (bpow (ex - 1) <= Rabs x < bpow ex)%R -> canonic_exponent x = fexp ex. Proof. intros x ex Hx. unfold canonic_exponent. now rewrite ln_beta_unique with (1 := Hx). Qed. Theorem mantissa_small_pos : forall x ex, (bpow (ex - 1) <= x < bpow ex)%R -> ... ... @@ -292,33 +277,6 @@ apply bpow_gt_0. now rewrite scaled_mantissa_bpow. Qed. Theorem generic_DN_pt_large_pos_ge_pow_aux : forall x ex, (fexp ex < ex)%Z -> (bpow (ex - 1) <= x)%R -> (bpow (ex - 1) <= F2R (Float beta (Zfloor (x * bpow (- fexp ex))) (fexp ex)))%R. Proof. intros x ex He1 Hx1. unfold F2R. simpl. replace (ex - 1)%Z with ((ex - 1 - fexp ex) + fexp ex)%Z by ring. rewrite bpow_add. apply Rmult_le_compat_r. apply bpow_ge_0. assert (Hx2 : bpow (ex - 1 - fexp ex) = Z2R (Zpower (radix_val beta) (ex - 1 - fexp ex))). apply sym_eq. apply Z2R_Zpower. omega. rewrite Hx2. apply Z2R_le. apply Zfloor_lub. rewrite <- Hx2. unfold Zminus at 1. rewrite bpow_add. apply Rmult_le_compat_r. apply bpow_ge_0. exact Hx1. Qed. Theorem generic_format_canonic : forall f, canonic f -> generic_format (F2R f). ... ...
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