Commit f656259a authored by Guillaume Melquiond's avatar Guillaume Melquiond

Finished proof of generic_format_succ.

parent c541aaa6
......@@ -166,8 +166,9 @@ unfold F, generic_format.
unfold scaled_mantissa, canonic_exponent.
rewrite ln_beta_unique with beta (x + ulp x)%R ex.
pattern x at 1 3 ; rewrite Fx.
unfold ulp, scaled_mantissa, canonic_exponent, F2R. simpl.
rewrite ln_beta_unique with (1 := Ex).
unfold ulp, scaled_mantissa.
rewrite canonic_exponent_fexp with (1 := Ex).
unfold F2R. simpl.
rewrite Rmult_plus_distr_r.
rewrite Rmult_assoc.
rewrite <- bpow_add, Zplus_opp_r, Rmult_1_r.
......@@ -190,7 +191,22 @@ apply bpow_ge_0.
rewrite H.
apply generic_format_bpow.
apply (prop_exp ex).
destruct (Zle_or_lt ex (fexp ex)) ; trivial.
elim Rlt_not_le with (1 := Zx).
rewrite Fx.
replace (Ztrunc (scaled_mantissa beta fexp x)) with Z0.
rewrite F2R_0.
apply Rle_refl.
unfold scaled_mantissa.
rewrite canonic_exponent_fexp with (1 := Ex).
destruct (mantissa_small_pos beta fexp x ex) ; trivial.
rewrite Ztrunc_floor.
apply sym_eq.
apply Zfloor_imp.
now apply Rlt_le.
exact H2.
now apply Rlt_le.
now apply Rlt_le.
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