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_nil_x x : FRACTRAN_HALTING (nil,x) <-> True.