(* ** Multiplication *)
Arguments mult : simpl never.
Arguments plus : simpl never.
(* *** Addition *)
Definition Add_Step : pTM sigNat^+ (option unit) 2 :=
If (CaseNat @ [|Fin1|])
(Return (Constr_S @ [|Fin0|]) None)
(Return Nop (Some tt)).
Definition Add_Step_steps : nat := 9.
Definition Add_Step_size (a b : nat) : Vector.t (nat->nat) 2 :=
match b with
| 0 => [|id; id|]
| S b' => [|S; S|]
end.

Lemma Add_Step_SpecT_space (a b : nat) (ss : Vector.t nat 2) :
TripleT
(≃≃([],  withSpace ( [|Contains _ a; Contains _ b|]) ss))
Add_Step_steps
Add_Step
(fun yout =>
≃≃([yout = if b then Some tt else None]
,withSpace [|Contains _ (match b with 0 => a | _ => S a end);Contains _ (pred b)|]
(appSize (Add_Step_size a b) ss))).