Commit 750219e4 authored by BOLDO Sylvie's avatar BOLDO Sylvie

Still about pred

parent f26588e6
......@@ -847,6 +847,7 @@ Qed.
Theorem pred_lt:
forall x,
(pred x < x)%R.
unfold pred.
case Req_bool_spec; intros H.
......@@ -908,12 +909,45 @@ now apply Heps.
Theorem succ_lt_le:
Theorem le_pred_lt:
forall x y,
F x -> F y ->
(0 < x < y)%R ->
(x + ulp x <= y)%R.
intros x y Hx Hy H. *)
(x <= pred y)%R.
intros x y Hx Hy H.
(* *)
assert (0 < pred y)%R.
(* *)
case (Rle_or_lt (ulp (pred y)) (y-x)); intros H1.
(* *)
apply Rplus_le_reg_r with (-x + ulp (pred y))%R.
ring_simplify (x+(-x+ulp (pred y)))%R.
apply Rle_trans with (1:=H1).
rewrite <- (pred_ulp y) at 1; trivial.
apply Req_le; ring.
apply Rlt_trans with (1:=proj1 H); easy.
now apply Rgt_not_eq.
(* *)
replace x with (y-(y-x))%R by ring.
rewrite <- rounding_DN_pred with (eps:=(y-x)%R); try easy.
ring_simplify (y-(y-x))%R.
apply Req_le.
apply sym_eq; now apply rounding_generic.
split; trivial.
now apply Rlt_Rminus.
now apply Rlt_le.
End Fcore_ulp.
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