renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma
index 61483a73d37d79375541076c27044bef5a8ddc3b..b3a07339bbe3bedba4333fccdfde4b04cceb9b10 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/functions/append_2.ma".
+include "basic_2/notation/functions/snitem_2.ma".
 include "basic_2/notation/functions/snbind1_2.ma".
 include "basic_2/notation/functions/snbind2_3.ma".
 include "basic_2/notation/functions/snvoid_1.ma".
@@ -23,62 +23,78 @@ include "basic_2/syntax/lenv.ma".
 (* APPEND FOR LOCAL ENVIRONMENTS ********************************************)
 
 rec definition append L K on K ≝ match K with
-[ LAtom       ⇒ L
-| LPair K I V ⇒ (append L K).ⓑ{I}V
+[ LAtom     ⇒ L
+| LBind K I ⇒ (append L K).ⓘ{I}
 ].
 
-interpretation "append (local environment)" 'Append L1 L2 = (append L1 L2).
-(*
+interpretation "append (local environment)" 'plus L1 L2 = (append L1 L2).
+
+interpretation "local environment tail binding construction (generic)"
+   'SnItem I L = (append (LBind LAtom I) L).
+
 interpretation "local environment tail binding construction (unary)"
-   'SnBind1 I L = (append (LUnit LAtom I) L).
-*)
+   'SnBind1 I L = (append (LBind LAtom (BUnit I)) L).
+
 interpretation "local environment tail binding construction (binary)"
-   'SnBind2 I T L = (append (LPair LAtom I T) L).
-(*
+   'SnBind2 I T L = (append (LBind LAtom (BPair I T)) L).
+
 interpretation "tail exclusion (local environment)"
-   'SnVoid L = (append (LUnit LAtom Void) L).
-*)
+   'SnVoid L = (append (LBind LAtom (BUnit Void)) L).
+
 interpretation "tail abbreviation (local environment)"
-   'SnAbbr T L = (append (LPair LAtom Abbr T) L).
+   'SnAbbr T L = (append (LBind LAtom (BPair Abbr T)) L).
 
 interpretation "tail abstraction (local environment)"
-   'SnAbst L T = (append (LPair LAtom Abst T) L).
+   'SnAbst L T = (append (LBind LAtom (BPair 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: ∀L. L @@ ⋆ = L.
+lemma append_atom: ∀L. (L + ⋆) = L. (**) (* () should be redundant *)
 // qed.
 
-lemma append_pair: ∀I,L,K,V. L@@(K.ⓑ{I}V) = (L@@K).ⓑ{I}V.
+(* Basic_2A1: uses: append_pair *)
+lemma append_bind: ∀I,L,K. L+(K.ⓘ{I}) = (L+K).ⓘ{I}.
 // qed.
 
-lemma append_atom_sn: ∀L. ⋆@@L = L.
+lemma append_atom_sn: ∀L. ⋆ + L = L.
 #L elim L -L //
-#L #I #V >append_pair //
+#L #I >append_bind //
 qed.
 
 lemma append_assoc: associative … append.
 #L1 #L2 #L3 elim L3 -L3 //
 qed.
 
-lemma append_shift: ∀L,K,I,V. L@@(ⓑ{I}V.K) = (L.ⓑ{I}V)@@K.
-#L #K #I #V <append_assoc //
+lemma append_shift: ∀L,K,I. L+(ⓘ{I}.K) = (L.ⓘ{I})+K.
+#L #K #I <append_assoc //
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma append_inj_sn: ∀K,L1,L2. L1@@K = L2@@K → L1 = L2.
+lemma append_inv_atom3_sn: ∀L,K. ⋆ = L + K → ∧∧ ⋆ = L & ⋆ = K.
+#L * /2 width=1 by conj/
+#K #I >append_bind #H destruct
+qed-.
+
+lemma append_inv_bind3_sn: ∀I0,L,L0,K. L0.ⓘ{I0} = L + K →
+                           ∨∨ ∧∧ L0.ⓘ{I0} = L & ⋆ = K
+                            | ∃∃K0. K = K0.ⓘ{I0} & L0 = L + K0.
+#I0 #L #L0 * /3 width=1 by or_introl, conj/
+#K #I >append_bind #H destruct /3 width=3 by ex2_intro, or_intror/
+qed-.
+
+lemma append_inj_sn: ∀K,L1,L2. L1+K = L2+K → L1 = L2.
 #K elim K -K //
-#K #I #V #IH #L1 #L2 >append_pair #H
-elim (destruct_lpair_lpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
+#K #I #IH #L1 #L2 >append_bind #H
+elim (destruct_lbind_lbind_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
 qed-.
 
 (* Basic_1: uses: chead_ctail *)
 (* Basic_2A1: uses: lpair_ltail *)
-lemma lenv_case_tail: ∀L. L = ⋆ ∨ ∃∃K,I,V. L = ⓑ{I}V.K.
+lemma lenv_case_tail: ∀L. L = ⋆ ∨ ∃∃K,I. L = ⓘ{I}.K.
 #L elim L -L /2 width=1 by or_introl/
-#L #I #V * [2: * ] /3 width=4 by ex1_3_intro, or_intror/
+#L #I * [2: * ] /3 width=3 by ex1_2_intro, or_intror/
 qed-.