+(* Properties with iterated push ********************************************)
+
+lemma isid_pushs: ∀n,f. 𝐈❪f❫ → 𝐈❪⫯*[n]f❫.
+#n elim n -n /3 width=3 by isid_push/
+qed.
+
+(* Inversion lemmas with iterated push **************************************)
+
+lemma isid_inv_pushs: ∀n,g. 𝐈❪⫯*[n]g❫ → 𝐈❪g❫.
+#n elim n -n /3 width=3 by isid_inv_push/
+qed.
+