-lemma at_plus2: ∀f,i1,i,n,m. @⦃i1, n@f⦄ ≡ i → @⦃i1, (m+n)@f⦄ ≡ m+i.
-#f #i1 #i #n #m #H elim m -m /2 width=5 by at_next/
+lemma at_plus2: ∀f,i1,i,n,m. @⦃i1, n⨮f⦄ ≘ i → @⦃i1, (m+n)⨮f⦄ ≘ m+i.
+#f #i1 #i #n #m #H elim m -m //
+#m <plus_S1 /2 width=5 by at_next/ (**) (* full auto fails *)