From Undecidability.L Require Import InterpreterResults.
(** ** Parallel or *)
Definition H (s t : term) : term := Eval cbv in (.\ "z"; !E "z" !s !(lambda T) (!E "z" !t !(lambda T) !F)).
Definition O : term := Eval cbv in .\ "x", "y";
(.\ "z"; !E "z" "x" !(lambda T) (!E "z" "y" !(lambda F) !I)) (!C !(H 2 1)).

Lemma O_rec s t : O (tenc s) (tenc t) ≡ (lambda (E 0 (tenc s) (lambda T) (E 0 (tenc t) (lambda F) I))) (C (H (tenc s) (tenc t))).