Class Inhabitant (A: Type) := default : A.
Instance Inhabitant_Z : Inhabitant Z := 0.
Instance Inhabitant_nat : Inhabitant nat := O.
Instance Inhabitant_positive : Inhabitant positive := 1%positive.
Instance Inhabitant_list {T: Type} : Inhabitant (list T) := @nil T.
Instance Inhabitant_fun {T1 T2: Type} {H: Inhabitant T2} : Inhabitant (T1->T2) := fun _ => H.
Instance Inhabitant_Prop : Inhabitant Prop := False.
Instance Inhabitant_bool : Inhabitant bool := false.
Instance Inhabitant_pair {T1 T2 : Type} {x1: Inhabitant T1} {x2: Inhabitant T2} : Inhabitant (T1*T2)%type := (x1,x2).

Lemma list_repeat_app: forall A a b (x:A),
list_repeat a x ++ list_repeat b x = list_repeat (a+b) x.