#j #Hg elim (pr_pat_inv_next ā¦ Hg ā¦ H) -Hg -H /2 width=2 by ex_intro/
qed-.
+(* Basic constructions ******************************************************)
+
+lemma pr_ist_push (f): šāŖfā« ā šāŖā«Æfā«.
+#f #Hf *
+[ /3 width=2 by pr_pat_refl, ex_intro/
+| #i elim (Hf i) -Hf /3 width=8 by pr_pat_push, ex_intro/
+]
+qed.
+
+lemma pr_ist_next (f): šāŖfā« ā šāŖāfā«.
+#f #Hf #i elim (Hf i) -Hf
+/3 width=6 by pr_pat_next, ex_intro/
+qed.
+
(* Constructions with pr_tl *************************************************)
(*** istot_tl *)