Section Fprop_plus_mult_ulp.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable fexp : Z -> Z.
Context { valid_exp : Valid_exp fexp }.
Context { monotone_exp : Monotone_exp fexp }.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
Notation format := (generic_format beta fexp).
Notation cexp := (cexp beta fexp).

Lemma ex_shift :
forall x e, format x -> (e <= cexp x)%Z ->
exists m, (x = IZR m * bpow e)%R.