let initial = newproof in
Equality.build_goal_proof goalproof initial type_of_goal side_effects
in
+prerr_endline (CicPp.pp goal_proof names);
let goal_proof = Subst.apply_subst subsumption_subst goal_proof in
let side_effects_t =
List.map (Subst.apply_subst subsumption_subst) side_effects_t