update in ground, basic_2A and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / grammar / lenv_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/grammar/lenv_append.ma b/matita/matita/contribs/lambdadelta/basic_2A/grammar/lenv_append.ma
index 6ac04a83d833be62cab5fe47c532228bddee926b..e11e641ec2ffd18b2aae96079de7ad92a02dc02c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2A/grammar/lenv_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2A/grammar/lenv_append.ma
@@ -42,11 +42,11 @@ interpretation
   '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.
 
@@ -54,7 +54,7 @@ lemma append_assoc: associative … append.
 #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.
 
@@ -71,7 +71,7 @@ qed-.
 
 (* 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/
@@ -86,7 +86,7 @@ lemma append_inj_sn: ∀K1,K2,L1,L2. L1 ;; K1 = L2 ;; K2 → |K1| = |K2| →
 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/
@@ -104,11 +104,11 @@ lemma append_inj_dx: ∀K1,K2,L1,L2. L1 ;; K1 = L2 ;; K2 → |L1| = |L2| →
 ]
 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-.