proposition: Lemma phi_compare63_compat u1 u2 v1 v2 : to_Z u1 = to_Z u2 -> to_Z v1 = to_Z v2 -> u1 ?= v1 = (u2 ?= v2).
proof: Proof. intros Hu1 Hv1. generalize (phi_compare63 u1 v1) (phi_compare63 u2 v2); do 2 case compare; auto; intros H1 H2; contradict H2; auto with zarith. Qed.
imports: PrimInt63 Cyclic63 List BasicRubik