interpretation "tail abstraction (local environment)"
'SnAbst L T = (append (LPair LAtom Abst T) L).
-definition l_appendable_sn: predicate (lenv→relation term) ≝ λR.
+definition d_appendable_sn: predicate (lenv→relation term) ≝ λR.
∀K,T1,T2. R K T1 T2 → ∀L. R (L @@ K) T1 T2.
(* Basic properties *********************************************************)
| #K1 #I1 #V1 #IH * normalize
[ #L1 #L2 #_ <plus_n_Sm #H destruct
| #K2 #I2 #V2 #L1 #L2 #H1 #H2
- elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
+ elim (destruct_lpair_lpair_aux … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
elim (IH … H1) -IH -H1 /2 width=1 by conj/
]
]
normalize in H2; >append_length in H2; #H
elim (plus_xySz_x_false … (sym_eq … H))
| #K2 #I2 #V2 #L1 #L2 #H1 #H2
- elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
+ elim (destruct_lpair_lpair_aux … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
elim (IH … H1) -IH -H1 /2 width=1 by conj/
]
]
#I #L #K #V #H elim (append_inj_dx … (⋆.ⓑ{I}V) … H) //
qed-.
-lemma length_inv_pos_dx_ltail: ∀L,d. |L| = d + 1 →
- ∃∃I,K,V. |K| = d & L = ⓑ{I}V.K.
-#Y #d #H elim (length_inv_pos_dx … H) -H #I #L #V #Hd #HLK destruct
+lemma length_inv_pos_dx_ltail: ∀L,l. |L| = l + 1 →
+ ∃∃I,K,V. |K| = l & L = ⓑ{I}V.K.
+#Y #l #H elim (length_inv_pos_dx … H) -H #I #L #V #Hl #HLK destruct
elim (lpair_ltail L I V) /2 width=5 by ex2_3_intro/
qed-.
-lemma length_inv_pos_sn_ltail: ∀L,d. d + 1 = |L| →
- ∃∃I,K,V. d = |K| & L = ⓑ{I}V.K.
-#Y #d #H elim (length_inv_pos_sn … H) -H #I #L #V #Hd #HLK destruct
+lemma length_inv_pos_sn_ltail: ∀L,l. l + 1 = |L| →
+ ∃∃I,K,V. l = |K| & L = ⓑ{I}V.K.
+#Y #l #H elim (length_inv_pos_sn … H) -H #I #L #V #Hl #HLK destruct
elim (lpair_ltail L I V) /2 width=5 by ex2_3_intro/
qed-.