Section TRANSF_PARTIAL_PROGRAM.
Variable A B V: Type.
Variable transf_fun: A -> res B.
Definition transform_partial_program (p: program A V) : res (program B V) :=
transform_partial_program2 (fun i f => transf_fun f) (fun i v => OK v) p.
End TRANSF_PARTIAL_PROGRAM.

Lemma transform_program_partial_program:
forall (A B V: Type) (transf_fun: A -> B) (p: program A V),
transform_partial_program (fun f => OK (transf_fun f)) p = OK (transform_program transf_fun p).