lemma length_inv_zero_sn: ∀L. 0 = |L| → L = ⋆.
/2 width=1 by length_inv_zero_dx/ qed-.
-lemma length_inv_pos_dx: ∀n,L. |L| = ⫯n →
- ∃∃I,K,V. |K| = n & L = K. ⓑ{I}V.
+(* Basic_2A1: was: length_inv_pos_dx *)
+lemma length_inv_succ_dx: ∀n,L. |L| = ⫯n →
+ ∃∃I,K,V. |K| = n & L = K. ⓑ{I}V.
#n * /3 width=5 by injective_S, ex2_3_intro/
>length_atom #H destruct
qed-.
-lemma length_inv_pos_sn: ∀n,L. ⫯n = |L| →
- ∃∃I,K,V. n = |K| & L = K. ⓑ{I}V.
+(* Basic_2A1: was: length_inv_pos_sn *)
+lemma length_inv_succ_sn: ∀n,L. ⫯n = |L| →
+ ∃∃I,K,V. n = |K| & L = K. ⓑ{I}V.
#l #L #H lapply (sym_eq ??? H) -H
-#H elim (length_inv_pos_dx … H) -H /2 width=5 by ex2_3_intro/
+#H elim (length_inv_succ_dx … H) -H /2 width=5 by ex2_3_intro/
qed-.
(* Basic_2A1: removed theorems 1: length_inj *)