Weaken hypothesis of le_pred_lt.

src/Core/Fcore_ulp.v

@@ -918,7 +918,7 @@ apply Ropp_lt_contravar.
 now apply Heps.
 Qed.
 
-Theorem le_pred_lt:
+Theorem le_pred_lt_aux :
   forall x y,
   F x -> F y ->
   (0 < x < y)%R ->
@@ -1033,4 +1033,19 @@ now apply Rlt_Rminus.
 now apply Rlt_le.
 Qed.
 
+Theorem le_pred_lt :
+  forall x y,
+  F x -> F y ->
+  (0 < y)%R ->
+  (x < y)%R ->
+  (x <= pred y)%R.
+Proof.
+intros x y Fx Fy Hy Hxy.
+destruct (Rle_or_lt x 0) as [Hx|Hx].
+apply Rle_trans with (1 := Hx).
+now apply pred_ge_0.
+apply le_pred_lt_aux ; try easy.
+now split.
+Qed.
+
 End Fcore_ulp.