-let corec at_ext: ∀f1,f2. 𝐓⦃f1⦄ → 𝐓⦃f2⦄ →
- (∀i,i1,i2. @⦃i, f1⦄ ≡ i1 → @⦃i, f2⦄ ≡ i2 → i1 = i2) → f1 ≗ f2 ≝ ?.
+lemma istot_tl: ∀f. 𝐓❪f❫ → 𝐓❪⫱f❫.
+#f cases (pn_split f) *
+#g * -f /2 width=3 by istot_inv_next, istot_inv_push/
+qed.
+
+(* Properties on tls ********************************************************)
+
+lemma istot_tls: ∀n,f. 𝐓❪f❫ → 𝐓❪⫱*[n]f❫.
+#n elim n -n /3 width=1 by istot_tl/
+qed.
+
+(* Main forward lemmas on at ************************************************)
+
+corec theorem at_ext: ∀f1,f2. 𝐓❪f1❫ → 𝐓❪f2❫ →
+ (∀i,i1,i2. @❪i,f1❫ ≘ i1 → @❪i,f2❫ ≘ i2 → i1 = i2) →
+ f1 ≡ f2.