Commit 9e494218 by Guillaume Melquiond

### Simplify proof.

parent 056b214a
 ... ... @@ -284,28 +284,14 @@ rewrite IZR_Zpower. rewrite <- bpow_plus; f_equal; ring. Qed. Lemma mag_minus1: forall z, (z<>0)%R -> (mag beta z -1 = mag beta (z / IZR beta))%Z. Lemma mag_minus1 : forall z, z <> 0%R -> (mag beta z - 1)%Z = mag beta (z / IZR beta). Proof with auto with typeclass_instances. intros z Hz; apply sym_eq, mag_unique. destruct (mag beta z) as (e,He); simpl. replace (z / IZR beta)%R with (z*bpow (-1))%R. rewrite Rabs_mult, (Rabs_right (bpow _)); try split. apply Rmult_le_reg_r with (bpow 1). apply bpow_gt_0. rewrite Rmult_assoc, <- 2!bpow_plus. rewrite Rmult_1_r. apply Rle_trans with (2:=proj1 (He Hz)). apply bpow_le; omega. apply Rmult_lt_reg_r with (bpow 1). apply bpow_gt_0. rewrite Rmult_assoc, <- 2!bpow_plus. rewrite Rmult_1_r. apply Rlt_le_trans with (1:=proj2 (He Hz)). apply bpow_le; omega. apply Rle_ge, bpow_ge_0. simpl; unfold Rdiv; f_equal; f_equal; f_equal. unfold Z.pow_pos; simpl; ring. intros z Hz. unfold Zminus. rewrite <- mag_mult_bpow by easy. now rewrite bpow_opp, bpow_1. Qed. Theorem round_plus_F2R : ... ...
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