Notation " x *X* y " := (mprod _ x y) (at level 40, no associativity): vector_scope.
Section Trans.
Variable p p1 : eparams.
Hypothesis Hp: vparamsProp p.
Hypothesis Hp1: vparamsProp p1.
Variable (f: p -> p1).
Variable (g : stype p -> stype p1).
Variable (g1 : stype p1 -> stype p).
Hypothesis Hf0: f 0%v = 0%v.
Hypothesis Hf1: forall x y : p, (f (x + y) = f x + f y)%v.
Hypothesis Hf2: forall (k: stype p) (x : p), (f (k .* x) = g k .* f x)%v.
Hypothesis Hg: forall k, g (g1 k) = k.

(* Specifications: *)
Lemma cbl_map l v : cbl _ l v -> cbl _ (map f l) (f v).
Lemma cbl_map_inv l v :
cbl _ (map f l) v -> exists v1, cbl _ l v1 /\ v = f v1.