(* *)
(**************************************************************************)
-include "ground_2/notation/functions/append_2.ma".
+include "ground/notation/functions/double_semicolon_2.ma".
include "basic_2A/notation/functions/snbind2_3.ma".
include "basic_2A/notation/functions/snabbr_2.ma".
include "basic_2A/notation/functions/snabst_2.ma".
| LPair K I V ⇒ (append L K). ⓑ{I} V
].
-interpretation "append (local environment)" 'Append L1 L2 = (append L1 L2).
+interpretation
+ "append (local environment)"
+ 'DoubleSemicolon L1 L2 = (append L1 L2).
-interpretation "local environment tail binding construction (binary)"
- 'SnBind2 I T L = (append (LPair LAtom I T) L).
+interpretation
+ "local environment tail binding construction (binary)"
+ 'SnBind2 I T L = (append (LPair LAtom I T) L).
-interpretation "tail abbreviation (local environment)"
- 'SnAbbr T L = (append (LPair LAtom Abbr T) L).
+interpretation
+ "tail abbreviation (local environment)"
+ 'SnAbbr T L = (append (LPair LAtom Abbr T) L).
-interpretation "tail abstraction (local environment)"
- 'SnAbst L T = (append (LPair LAtom Abst T) L).
+interpretation
+ "tail abstraction (local environment)"
+ 'SnAbst L T = (append (LPair LAtom Abst T) L).
definition d_appendable_sn: predicate (lenv→relation term) ≝ λR.
- ∀K,T1,T2. R K T1 T2 → ∀L. R (L @@ K) T1 T2.
+ ∀K,T1,T2. R K T1 T2 → ∀L. R (L ● K) T1 T2.
(* Basic properties *********************************************************)
-lemma append_atom_sn: ∀L. ⋆ @@ L = L.
+lemma append_atom_sn: ∀L. ⋆ ● L = L.
#L elim L -L normalize //
qed.
#L1 #L2 #L3 elim L3 -L3 normalize //
qed.
-lemma append_length: ∀L1,L2. |L1 @@ L2| = |L1| + |L2|.
+lemma append_length: ∀L1,L2. |L1 ● L2| = |L1| + |L2|.
#L1 #L2 elim L2 -L2 normalize //
qed.
#I #L #V >append_length //
qed.
-(* Basic_1: was just: chead_ctail *)
lemma lpair_ltail: ∀L,I,V. ∃∃J,K,W. L.ⓑ{I}V = ⓑ{J}W.K & |L| = |K|.
#L elim L -L /2 width=5 by ex2_3_intro/
#L #Z #X #IHL #I #V elim (IHL Z X) -IHL
(* Basic inversion lemmas ***************************************************)
-lemma append_inj_sn: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |K1| = |K2| →
+lemma append_inj_sn: ∀K1,K2,L1,L2. L1 ● K1 = L2 ● K2 → |K1| = |K2| →
L1 = L2 ∧ K1 = K2.
#K1 elim K1 -K1
[ * normalize /2 width=1 by conj/
qed-.
(* Note: lemma 750 *)
-lemma append_inj_dx: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |L1| = |L2| →
+lemma append_inj_dx: ∀K1,K2,L1,L2. L1 ● K1 = L2 ● K2 → |L1| = |L2| →
L1 = L2 ∧ K1 = K2.
#K1 elim K1 -K1
[ * normalize /2 width=1 by conj/
]
qed-.
-lemma append_inv_refl_dx: ∀L,K. L @@ K = L → K = ⋆.
+lemma append_inv_refl_dx: ∀L,K. L ● K = L → K = ⋆.
#L #K #H elim (append_inj_dx … (⋆) … H) //
qed-.
-lemma append_inv_pair_dx: ∀I,L,K,V. L @@ K = L.ⓑ{I}V → K = ⋆.ⓑ{I}V.
+lemma append_inv_pair_dx: ∀I,L,K,V. L ● K = L.ⓑ{I}V → K = ⋆.ⓑ{I}V.
#I #L #K #V #H elim (append_inj_dx … (⋆.ⓑ{I}V) … H) //
qed-.
(* Basic eliminators ********************************************************)
-(* Basic_1: was: c_tail_ind *)
lemma lenv_ind_alt: ∀R:predicate lenv.
R (⋆) → (∀I,L,T. R L → R (ⓑ{I}T.L)) →
∀L. R L.