X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Fappend_length.ma;h=c1133e8c0fba47afcb25f4ce04f0180c58b3158d;hb=a77d0bd6a04e94f765d329d47b37d9e04d349b14;hp=043f1be8904b56194e78849e9f578814eea58dad;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4;p=helm.git

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 043f1be89..c1133e8c0 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/append_length.ma
@@ -19,19 +19,19 @@ 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.
 
-lemma ltail_length: ∀I,L. |ⓘ{I}.L| = ⫯|L|.
+lemma ltail_length: ∀I,L. |ⓘ{I}.L| = ↑|L|.
 #I #L >append_length //
 qed.
 
 (* Advanced inversion lemmas on length for local environments ***************)
 
 (* Basic_2A1: was: length_inv_pos_dx_ltail *)
-lemma length_inv_succ_dx_ltail: ∀L,n. |L| = ⫯n →
+lemma length_inv_succ_dx_ltail: ∀L,n. |L| = ↑n →
                                 ∃∃I,K. |K| = n & L = ⓘ{I}.K.
 #Y #n #H elim (length_inv_succ_dx … H) -H #I #L #Hn #HLK destruct
 elim (lenv_case_tail … L) [2: * #K #J ]
@@ -39,7 +39,7 @@ elim (lenv_case_tail … L) [2: * #K #J ]
 qed-.
 
 (* Basic_2A1: was: length_inv_pos_sn_ltail *)
-lemma length_inv_succ_sn_ltail: ∀L,n. ⫯n = |L| →
+lemma length_inv_succ_sn_ltail: ∀L,n. ↑n = |L| →
                                 ∃∃I,K. n = |K| & L = ⓘ{I}.K.
 #Y #n #H elim (length_inv_succ_sn … H) -H #I #L #Hn #HLK destruct
 elim (lenv_case_tail … L) [2: * #K #J ]
@@ -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-.