Commit d40d74c2 authored by Guillaume Melquiond's avatar Guillaume Melquiond

Add theorem generic_format_abs_inv.

parent 5905eaba
......@@ -222,6 +222,20 @@ rewrite <- abs_F2R.
now apply f_equal.
Qed.
Theorem generic_format_abs_inv :
forall x, generic_format (Rabs x) -> generic_format x.
Proof.
intros x.
unfold generic_format, Rabs.
case Rcase_abs ; intros _.
rewrite scaled_mantissa_opp, canonic_exponent_opp, Ztrunc_opp.
intros H.
rewrite <- (Ropp_involutive x) at 1.
rewrite H, <- opp_F2R.
apply Ropp_involutive.
easy.
Qed.
Theorem canonic_exponent_fexp :
forall x ex,
(bpow (ex - 1) <= Rabs x < bpow ex)%R ->
......
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