unfold DistSingle_G2, DistSingle_G3_c2.
comp_swap_r.
comp_skip.
comp_simp.
comp_skip.
comp_skip.
eapply hybrid_replace_c2_equiv.
eapply RndNat_support_lt; intuition.
Qed.

Theorem DistSingle_G3_c1_equiv :
Pr[DistSingle_G2 c1] == Pr[DistSingle_G3_c1].