X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Fappend_length.ma;h=e7c79ebeeb2627e513618ca3dab1c9c992a2bd3e;hp=9291ba5d1ea77e4603cc5b340017f7bdbfe11088;hb=222044da28742b24584549ba86b1805a87def070;hpb=397413c4196f84c81d61ba7dd79b54ab1c428ebb

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma
index 9291ba5d1..e7c79ebee 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma
@@ -19,7 +19,7 @@ include "basic_2/syntax/append.ma".
 
 (* Properties with length for local environments ****************************)
 
-lemma append_length: ∀L1,L2. |L1 @@ L2| = |L1| + |L2|.
+lemma append_length: ∀L1,L2. |L1 + L2| = |L1| + |L2|.
 #L1 #L2 elim L2 -L2 //
 #L2 #I >append_bind >length_bind >length_bind //
 qed.
@@ -49,7 +49,7 @@ qed-.
 (* Inversion lemmas with length for local environments **********************)
 
 (* Basic_2A1: was: append_inj_sn *)
-lemma append_inj_length_sn: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |K1| = |K2| →
+lemma append_inj_length_sn: ∀K1,K2,L1,L2. L1 + K1 = L2 + K2 → |K1| = |K2| →
                             L1 = L2 ∧ K1 = K2.
 #K1 elim K1 -K1
 [ * /2 width=1 by conj/
@@ -67,7 +67,7 @@ qed-.
 
 (* Note: lemma 750 *)
 (* Basic_2A1: was: append_inj_dx *)
-lemma append_inj_length_dx: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |L1| = |L2| →
+lemma append_inj_length_dx: ∀K1,K2,L1,L2. L1 + K1 = L2 + K2 → |L1| = |L2| →
                             L1 = L2 ∧ K1 = K2.
 #K1 elim K1 -K1
 [ * /2 width=1 by conj/
@@ -87,15 +87,15 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma append_inj_dx: ∀L,K1,K2. L@@K1 = L@@K2 → K1 = K2.
+lemma append_inj_dx: ∀L,K1,K2. L+K1 = L+K2 → K1 = K2.
 #L #K1 #K2 #H elim (append_inj_length_dx … H) -H //
 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-.
 
@@ -103,9 +103,9 @@ qed-.
 
 (* Basic_1: was: c_tail_ind *)
 (* Basic_2A1: was: lenv_ind_alt *) 
-lemma lenv_ind_tail: ∀R:predicate lenv.
-                     R (⋆) → (∀I,L. R L → R (ⓘ{I}.L)) → ∀L. R L.
-#R #IH1 #IH2 #L @(f_ind … length … L) -L #x #IHx * //
+lemma lenv_ind_tail: ∀Q:predicate lenv.
+                     Q (⋆) → (∀I,L. Q L → Q (ⓘ{I}.L)) → ∀L. Q L.
+#Q #IH1 #IH2 #L @(f_ind … length … L) -L #x #IHx * //
 #L #I -IH1 #H destruct
 elim (lenv_case_tail … L) [2: * #K #J ]
 #H destruct /3 width=1 by/