Section Interreducible.
Global Program Instance uni_sysuni (I: uni X): sysuni :=
{ Gammaᵤ' := Gammaᵤ; Eᵤ' := [(sᵤ, tᵤ)]; Lᵤ' := [Aᵤ]; Hᵤ' := _; }.
Global Program Instance sysuni_uni (I: sysuni): uni X :=
{
Gammaᵤ := Gammaᵤ';
sᵤ := linearize_terms (left_side Eᵤ');
tᵤ := linearize_terms (right_side Eᵤ');
Aᵤ := (Arr (rev Lᵤ') alpha) → alpha;
H1ᵤ := _;
H2ᵤ := _;
}.

Lemma SU_U: SU ⪯ U X.