Commit a229b3ea authored by Guillaume Melquiond's avatar Guillaume Melquiond

Added generic_format_ge_bpow.

parent 6c02f641
......@@ -347,6 +347,23 @@ rewrite Rmult_assoc, <- bpow_plus, Zplus_opp_r, Rmult_1_r.
now rewrite Ztrunc_Z2R.
Theorem generic_format_ge_bpow :
forall emin,
( forall e, (emin <= fexp e)%Z ) ->
forall x,
(0 < x)%R ->
generic_format x ->
(bpow emin <= x)%R.
intros emin Emin x Hx Fx.
rewrite Fx.
apply Rle_trans with (bpow (fexp (ln_beta beta x))).
now apply bpow_le.
apply bpow_le_F2R.
apply F2R_gt_0_reg with beta (canonic_exponent x).
now rewrite <- Fx.
Theorem canonic_exp_ge:
forall prec,
(forall e, (e - fexp e <= prec)%Z) ->
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