proposition: Lemma R_one_singleton_emptyset : R 1 = singleton emptyset.
proof: Proof. ap extensionality; uhg; ir. rwi nat_realization_S H. nin H. rwi nat_zero_emptyset H. nin (B H). rwi nat_zero_emptyset H. rw H. ap singleton_inc. rw nat_realization_S. ap or_intror. cp (singleton_eq H). rw nat_zero_emptyset; am. Qed.
imports: tactics