intros p q r H H0 H1.
case (Req_dec r 0); intros Hr.
replace (Rabs (r - (p + q))) with (Rabs r * / 2%nat * 0)%R.
apply Rmult_le_compat_l.
replace 0%R with (Rabs r * 0)%R; [ apply Rmult_le_compat_l | ring ];
auto with real arith.
replace 0%R with (radix * 0)%R; [ apply Rmult_le_compat_l | ring ];
auto with real arith.
apply Rlt_le; apply Rinv_0_lt_compat; auto with real arith.
replace 0%R with (IZR 0%nat); auto with real zarith; apply Rlt_IZR.
apply Zle_lt_trans with (nNormMin radix precision).
apply Zlt_le_weak; apply nNormPos; auto with real zarith.
apply nNormMimLtvNum; auto with real zarith.
rewrite <- plusExactR0 with (3 := H1); auto with real zarith.
rewrite Hr; repeat rewrite Rabs_R0 || (rewrite Rminus_diag_eq; auto); ring.
apply Rlt_le; apply plusErrorBound1; auto.
Contradict Hr; unfold FtoRradix in |- *; apply is_Fzero_rep1; auto.
Qed.

(* Specifications: *)
Theorem pPredMoreThanOne : (0 < pPred (vNum b))%Z.
unfold pPred in |- *; apply Zlt_succ_pred; simpl in |- *.