Fact fractran_step_no_zero_num l : Forall (fun c => fst c <> 0) l -> forall x y, l // x → y -> y = 0 -> x = 0.
Fact fractran_rt_no_zero_den l n y : fractran_regular l -> fractran_steps l n 0 y -> y = 0.
Fact fractran_rt_no_zero_num l : Forall (fun c => fst c <> 0) l -> forall n x, fractran_steps l n x 0 -> x = 0.
Fact fractran_zero_num l x : Exists (fun c => fst c = 0) l -> exists y, l // x → y.

Lemma FRACTRAN_HALTING_l_1_no_zero_den l x :
l <> nil
-> x <> 0
-> Forall (fun c => fst c <> 0) l
-> FRACTRAN_HALTING (l,x) <-> FRACTRAN_HALTING (remove_zero_den l,x).