Notation bpow e := (bpow beta e).Notation format := (generic_format beta fexp).

Theorem inbetween_float_round : forall rnd choice, ( forall x m l, inbetween_int m x l -> rnd x = choice m l ) -> forall x m l, let e := canonic_exp beta fexp x in inbetween_float beta m e x l -> round beta fexp rnd x = F2R (Float beta (choice m l) e).