// qed.
(* Basic_2A1: uses: length_pair *)
-lemma length_bind: ∀I,L. |L.ⓘ{I}| = ↑|L|.
+lemma length_bind: ∀I,L. |L.ⓘ[I]| = ↑|L|.
// qed.
(* Basic inversion lemmas ***************************************************)
(* Basic_2A1: was: length_inv_pos_dx *)
lemma length_inv_succ_dx: ∀n,L. |L| = ↑n →
- ∃∃I,K. |K| = n & L = K. ⓘ{I}.
+ ∃∃I,K. |K| = n & L = K. ⓘ[I].
#n *
[ >length_atom #H destruct
-| #L #I >length_bind /3 width=4 by ex2_2_intro, injective_S/
+| #L #I >length_bind /3 width=4 by ex2_2_intro, eq_inv_nsucc_bi/
]
qed-.
(* Basic_2A1: was: length_inv_pos_sn *)
lemma length_inv_succ_sn: ∀n,L. ↑n = |L| →
- ∃∃I,K. n = |K| & L = K. ⓘ{I}.
-#n #L #H lapply (sym_eq ??? H) -H
+ ∃∃I,K. n = |K| & L = K. ⓘ[I].
+#n #L #H lapply (sym_eq ??? H) -H
#H elim (length_inv_succ_dx … H) -H /2 width=4 by ex2_2_intro/
qed-.