Section fractran_mma_reg_reduction.
Variables (ll : list (nat*nat)).
Let reduction : { P | Forall (fun c => snd c <> 0) ll -> forall x, ll /F/ x ↓ <-> (1,P) /MM2/ (1,x##0##vec_nil) ↓ }.
Definition fractran_reg_mma := proj1_sig reduction.

Theorem fractran_reg_mma_reduction :
Forall (fun c => snd c <> 0) ll
-> forall x, ll /F/ x ↓
<-> (1,fractran_reg_mma) /MM2/ (1,x##0##vec_nil) ↓.