renaming in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq.ma
index e19708385f8b7d4fbcfdff2d99a4e7a5844adae3..9dd335a052d38be9ba50fe03d52160981b4534b2 100644 (file)
--- 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 (â\86\91n1) (K1.ⓧ) 0 K2
 | lveq_void_dx: ∀K1,K2,n2. lveq 0 K1 n2 K2 →
-                lveq 0 K1 (⫯n2) (K2.ⓧ)
+                lveq 0 K1 (â\86\91n2) (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 →
-                           â\88\80m1. ⫯m1 = n1 →
+                           â\88\80m1. â\86\91m1 = 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: â\88\80L1,K2,n1,n2. L1 â\89\8bâ\93§*[⫯n1, n2] K2 →
+lemma lveq_inv_succ_sn: â\88\80L1,K2,n1,n2. L1 â\89\8bâ\93§*[â\86\91n1, 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: â\88\80K1,L2,n1,n2. K1 â\89\8bâ\93§*[n1, ⫯n2] L2 →
+lemma lveq_inv_succ_dx: â\88\80K1,L2,n1,n2. K1 â\89\8bâ\93§*[n1, â\86\91n2] 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 →
-                        â\88\80m1,m2. ⫯m1 = n1 â\86\92 ⫯m2 = n2 → ⊥.
+                        â\88\80m1,m2. â\86\91m1 = n1 â\86\92 â\86\91m2 = 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
@@ -89,11 +89,16 @@ fact lveq_inv_succ_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
 ]
 qed-.
 
-lemma lveq_inv_succ: â\88\80L1,L2,n1,n2. L1 â\89\8bâ\93§*[⫯n1, ⫯n2] L2 → ⊥.
+lemma lveq_inv_succ: â\88\80L1,L2,n1,n2. L1 â\89\8bâ\93§*[â\86\91n1, â\86\91n2] L2 → ⊥.
 /2 width=9 by lveq_inv_succ_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma lveq_inv_bind: ∀I1,I2,K1,K2. K1.ⓘ{I1} ≋ⓧ*[0, 0] K2.ⓘ{I2} → K1 ≋ⓧ*[0, 0] K2.
+#I1 #I2 #K1 #K2 #H
+elim (lveq_inv_zero … H) -H * [| #Z1 #Z2 #Y1 #Y2 #HY ] #H1 #H2 destruct //
+qed-.
+  
 lemma lveq_inv_atom_atom: ∀n1,n2. ⋆ ≋ⓧ*[n1, n2] ⋆ → ∧∧ 0 = n1 & 0 = n2.
 * [2: #n1 ] * [2,4: #n2 ] #H
 [ elim (lveq_inv_succ … H)
@@ -104,7 +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] ⋆ →
-                          â\88\83â\88\83m1. K1 â\89\8bâ\93§*[m1, 0] â\8b\86 & BUnit Void = I1 & ⫯m1 = n1 & 0 = n2.
+                          â\88\83â\88\83m1. K1 â\89\8bâ\93§*[m1, 0] â\8b\86 & BUnit Void = I1 & â\86\91m1 = 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
@@ -117,7 +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} →
-                          â\88\83â\88\83m2. â\8b\86 â\89\8bâ\93§*[0, m2] K2 & BUnit Void = I2 & 0 = n1 & ⫯m2 = n2.
+                          â\88\83â\88\83m2. â\8b\86 â\89\8bâ\93§*[0, m2] K2 & BUnit Void = I2 & 0 = n1 & â\86\91m2 = n2.
 #I2 #K2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H
 elim (lveq_inv_bind_atom … H) -H
@@ -137,13 +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: â\88\80L1,L2,n1,n2. L1.â\93§ â\89\8bâ\93§*[⫯n1, n2] L2 →
+lemma lveq_inv_void_succ_sn: â\88\80L1,L2,n1,n2. L1.â\93§ â\89\8bâ\93§*[â\86\91n1, 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: â\88\80L1,L2,n1,n2. L1 â\89\8bâ\93§*[n1, ⫯n2] L2.ⓧ →
+lemma lveq_inv_void_succ_dx: â\88\80L1,L2,n1,n2. L1 â\89\8bâ\93§*[n1, â\86\91n2] L2.ⓧ →
                              ∧∧ L1 ≋ ⓧ*[0, n2] L2 & 0 = n1.
 #L1 #L2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H