proposition: Corollary reaches'E x y : reaches' x y -> exists n m, value1 y = value1 x + n /\ value2 y = value2 x + m /\ forall a b, (a > 0 -> value1 x > 0) -> (b > 0 -> value2 x > 0) -> reaches' (index x, (a, b)) (index y, (a + n, b + m)).
proof: Proof. move=> [k] /steps'E [n] [m] [?] [?] H. exists n, m. split; [done|split; [done|]]. move=> ????. exists k. by apply: H. Qed.
imports: List PeanoNat Lia Relation_Operators Operators_Properties Transitive_Closure Undecidability.MinskyMachines.MM2 Undecidability.MinskyMachines.Util.MM2_facts ssreflect ssrbool ssrfun