X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Flveq.ma;h=9dd335a052d38be9ba50fe03d52160981b4534b2;hp=524c2779b38549936a581c24d053cd8ccbdd490c;hb=222044da28742b24584549ba86b1805a87def070;hpb=b0eb62e60a2fd73ba39c7a0df112f04131528602

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma
index 524c2779b..9dd335a05 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma
@@ -22,9 +22,9 @@ inductive lveq: bi_relation nat lenv ≝
 | lveq_bind   : ∀I1,I2,K1,K2. lveq 0 K1 0 K2 →
                 lveq 0 (K1.ⓘ{I1}) 0 (K2.ⓘ{I2})
 | lveq_void_sn: ∀K1,K2,n1. lveq n1 K1 0 K2 →
-                lveq (⫯n1) (K1.ⓧ) 0 K2
+                lveq (↑n1) (K1.ⓧ) 0 K2
 | lveq_void_dx: ∀K1,K2,n2. lveq 0 K1 n2 K2 →
-                lveq 0 K1 (⫯n2) (K2.ⓧ)
+                lveq 0 K1 (↑n2) (K2.ⓧ)
 .
 
 interpretation "equivalence up to exclusion binders (local environment)"
@@ -60,7 +60,7 @@ lemma lveq_inv_zero: ∀L1,L2. L1 ≋ⓧ*[0, 0] L2 →
 /2 width=5 by lveq_inv_zero_aux/ qed-.
 
 fact lveq_inv_succ_sn_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                           ∀m1. ⫯m1 = n1 →
+                           ∀m1. ↑m1 = n1 →
                            ∃∃K1. K1 ≋ⓧ*[m1, 0] L2 & K1.ⓧ = L1 & 0 = n2.
 #L1 #L2 #n1 #n2 * -L1 -L2 -n1 -n2
 [1: #m #H destruct
@@ -69,11 +69,11 @@ fact lveq_inv_succ_sn_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
 ]
 qed-.
 
-lemma lveq_inv_succ_sn: ∀L1,K2,n1,n2. L1 ≋ⓧ*[⫯n1, n2] K2 →
+lemma lveq_inv_succ_sn: ∀L1,K2,n1,n2. L1 ≋ⓧ*[↑n1, n2] K2 →
                         ∃∃K1. K1 ≋ⓧ*[n1, 0] K2 & K1.ⓧ = L1 & 0 = n2.
 /2 width=3 by lveq_inv_succ_sn_aux/ qed-.
 
-lemma lveq_inv_succ_dx: ∀K1,L2,n1,n2. K1 ≋ⓧ*[n1, ⫯n2] L2 →
+lemma lveq_inv_succ_dx: ∀K1,L2,n1,n2. K1 ≋ⓧ*[n1, ↑n2] L2 →
                         ∃∃K2. K1 ≋ⓧ*[0, n2] K2 & K2.ⓧ = L2 & 0 = n1.
 #K1 #L2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H
@@ -81,7 +81,7 @@ elim (lveq_inv_succ_sn … H) -H /3 width=3 by lveq_sym, ex3_intro/
 qed-.
 
 fact lveq_inv_succ_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                        ∀m1,m2. ⫯m1 = n1 → ⫯m2 = n2 → ⊥.
+                        ∀m1,m2. ↑m1 = n1 → ↑m2 = n2 → ⊥.
 #L1 #L2 #n1 #n2 * -L1 -L2 -n1 -n2
 [1: #m1 #m2 #H1 #H2 destruct
 |2: #I1 #I2 #K1 #K2 #_ #m1 #m2 #H1 #H2 destruct
@@ -89,7 +89,7 @@ fact lveq_inv_succ_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
 ]
 qed-.
 
-lemma lveq_inv_succ: ∀L1,L2,n1,n2. L1 ≋ⓧ*[⫯n1, ⫯n2] L2 → ⊥.
+lemma lveq_inv_succ: ∀L1,L2,n1,n2. L1 ≋ⓧ*[↑n1, ↑n2] L2 → ⊥.
 /2 width=9 by lveq_inv_succ_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
@@ -109,7 +109,7 @@ lemma lveq_inv_atom_atom: ∀n1,n2. ⋆ ≋ⓧ*[n1, n2] ⋆ → ∧∧ 0 = n1 &
 qed-.
 
 lemma lveq_inv_bind_atom: ∀I1,K1,n1,n2. K1.ⓘ{I1} ≋ⓧ*[n1, n2] ⋆ →
-                          ∃∃m1. K1 ≋ⓧ*[m1, 0] ⋆ & BUnit Void = I1 & ⫯m1 = n1 & 0 = n2.
+                          ∃∃m1. K1 ≋ⓧ*[m1, 0] ⋆ & BUnit Void = I1 & ↑m1 = n1 & 0 = n2.
 #I1 #K1 * [2: #n1 ] * [2,4: #n2 ] #H
 [ elim (lveq_inv_succ … H)
 | elim (lveq_inv_succ_dx … H) -H #Y #_ #H1 #H2 destruct
@@ -122,7 +122,7 @@ lemma lveq_inv_bind_atom: ∀I1,K1,n1,n2. K1.ⓘ{I1} ≋ⓧ*[n1, n2] ⋆ →
 qed-.
 
 lemma lveq_inv_atom_bind: ∀I2,K2,n1,n2. ⋆ ≋ⓧ*[n1, n2] K2.ⓘ{I2} →
-                          ∃∃m2. ⋆ ≋ⓧ*[0, m2] K2 & BUnit Void = I2 & 0 = n1 & ⫯m2 = n2.
+                          ∃∃m2. ⋆ ≋ⓧ*[0, m2] K2 & BUnit Void = I2 & 0 = n1 & ↑m2 = n2.
 #I2 #K2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H
 elim (lveq_inv_bind_atom … H) -H
@@ -142,13 +142,13 @@ lemma lveq_inv_pair_pair: ∀I1,I2,K1,K2,V1,V2,n1,n2. K1.ⓑ{I1}V1 ≋ⓧ*[n1, n
 ]
 qed-.
 
-lemma lveq_inv_void_succ_sn: ∀L1,L2,n1,n2. L1.ⓧ ≋ⓧ*[⫯n1, n2] L2 →
+lemma lveq_inv_void_succ_sn: ∀L1,L2,n1,n2. L1.ⓧ ≋ⓧ*[↑n1, n2] L2 →
                              ∧∧ L1 ≋ ⓧ*[n1, 0] L2 & 0 = n2.
 #L1 #L2 #n1 #n2 #H
 elim (lveq_inv_succ_sn … H) -H #Y #HY #H1 #H2 destruct /2 width=1 by conj/
 qed-.
 
-lemma lveq_inv_void_succ_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, ⫯n2] L2.ⓧ →
+lemma lveq_inv_void_succ_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, ↑n2] L2.ⓧ →
                              ∧∧ L1 ≋ ⓧ*[0, n2] L2 & 0 = n1.
 #L1 #L2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H