Section Format.
Variable fexp : Z -> Z.
(** To be a good fexp *)
Class Valid_exp :=
valid_exp :
forall k : Z,
( (fexp k < k)%Z -> (fexp (k + 1) <= k)%Z ) /\
( (k <= fexp k)%Z ->
(fexp (fexp k + 1) <= fexp k)%Z /\
forall l : Z, (l <= fexp k)%Z -> fexp l = fexp k ).
Context { valid_exp_ : Valid_exp }.

Theorem valid_exp_large :
forall k l,
(fexp k < k)%Z -> (k <= l)%Z ->
(fexp l < l)%Z.