update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / mr2_at.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma
index 77aa3917cfd4138784d4d89d4c2b2fac71752af9..d2a2499a3af4dcc026edd9f30a79fb7766b388af 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma
@@ -20,9 +20,9 @@ include "ground_2/relocation/mr2.ma".
 inductive at: mr2 → relation nat ≝
 | at_nil: ∀i. at (◊) i i
 | at_lt : ∀cs,l,m,i1,i2. i1 < l →
-          at cs i1 i2 → at ({l, m};cs) i1 i2
+          at cs i1 i2 → at (❨l, m❩;cs) i1 i2
 | at_ge : ∀cs,l,m,i1,i2. l ≤ i1 →
-          at cs (i1 + m) i2 → at ({l, m};cs) i1 i2
+          at cs (i1 + m) i2 → at (❨l, m❩;cs) i1 i2
 .
 
 interpretation "application (multiple relocation with pairs)"
@@ -30,7 +30,7 @@ interpretation "application (multiple relocation with pairs)"
 
 (* Basic inversion lemmas ***************************************************)
 
-fact at_inv_nil_aux: â\88\80cs,i1,i2. @â¦\83i1, csâ¦\84 ≘ i2 → cs = ◊ → i1 = i2.
+fact at_inv_nil_aux: â\88\80cs,i1,i2. @â\9dªi1, csâ\9d« ≘ i2 → cs = ◊ → i1 = i2.
 #cs #i1 #i2 * -cs -i1 -i2
 [ //
 | #cs #l #m #i1 #i2 #_ #_ #H destruct
@@ -38,13 +38,13 @@ fact at_inv_nil_aux: ∀cs,i1,i2. @⦃i1, cs⦄ ≘ i2 → cs = ◊ → i1 = i2.
 ]
 qed-.
 
-lemma at_inv_nil: â\88\80i1,i2. @â¦\83i1, â\97\8aâ¦\84 ≘ i2 → i1 = i2.
+lemma at_inv_nil: â\88\80i1,i2. @â\9dªi1, â\97\8aâ\9d« ≘ i2 → i1 = i2.
 /2 width=3 by at_inv_nil_aux/ qed-.
 
-fact at_inv_cons_aux: â\88\80cs,i1,i2. @â¦\83i1, csâ¦\84 ≘ i2 →
-                      ∀l,m,cs0. cs = {l, m};cs0 →
-                      i1 < l â\88§ @â¦\83i1, cs0â¦\84 ≘ i2 ∨
-                      l â\89¤ i1 â\88§ @â¦\83i1 + m, cs0â¦\84 ≘ i2.
+fact at_inv_cons_aux: â\88\80cs,i1,i2. @â\9dªi1, csâ\9d« ≘ i2 →
+                      ∀l,m,cs0. cs = ❨l, m❩;cs0 →
+                      i1 < l â\88§ @â\9dªi1, cs0â\9d« ≘ i2 ∨
+                      l â\89¤ i1 â\88§ @â\9dªi1 + m, cs0â\9d« ≘ i2.
 #cs #i1 #i2 * -cs -i1 -i2
 [ #i #l #m #cs #H destruct
 | #cs1 #l1 #m1 #i1 #i2 #Hil1 #Hi12 #l2 #m2 #cs2 #H destruct /3 width=1 by or_introl, conj/
@@ -52,20 +52,20 @@ fact at_inv_cons_aux: ∀cs,i1,i2. @⦃i1, cs⦄ ≘ i2 →
 ]
 qed-.
 
-lemma at_inv_cons: â\88\80cs,l,m,i1,i2. @â¦\83i1, {l, m};csâ¦\84 ≘ i2 →
-                   i1 < l â\88§ @â¦\83i1, csâ¦\84 ≘ i2 ∨
-                   l â\89¤ i1 â\88§ @â¦\83i1 + m, csâ¦\84 ≘ i2.
+lemma at_inv_cons: â\88\80cs,l,m,i1,i2. @â\9dªi1, â\9d¨l, mâ\9d©;csâ\9d« ≘ i2 →
+                   i1 < l â\88§ @â\9dªi1, csâ\9d« ≘ i2 ∨
+                   l â\89¤ i1 â\88§ @â\9dªi1 + m, csâ\9d« ≘ i2.
 /2 width=3 by at_inv_cons_aux/ qed-.
 
-lemma at_inv_cons_lt: â\88\80cs,l,m,i1,i2. @â¦\83i1, {l, m};csâ¦\84 ≘ i2 →
-                      i1 < l â\86\92 @â¦\83i1, csâ¦\84 ≘ i2.
+lemma at_inv_cons_lt: â\88\80cs,l,m,i1,i2. @â\9dªi1, â\9d¨l, mâ\9d©;csâ\9d« ≘ i2 →
+                      i1 < l â\86\92 @â\9dªi1, csâ\9d« ≘ i2.
 #cs #l #m #i1 #m2 #H
 elim (at_inv_cons … H) -H * // #Hli1 #_ #Hi1l
 elim (lt_le_false … Hi1l Hli1)
 qed-.
 
-lemma at_inv_cons_ge: â\88\80cs,l,m,i1,i2. @â¦\83i1, {l, m};csâ¦\84 ≘ i2 →
-                      l â\89¤ i1 â\86\92 @â¦\83i1 + m, csâ¦\84 ≘ i2.
+lemma at_inv_cons_ge: â\88\80cs,l,m,i1,i2. @â\9dªi1, â\9d¨l, mâ\9d©;csâ\9d« ≘ i2 →
+                      l â\89¤ i1 â\86\92 @â\9dªi1 + m, csâ\9d« ≘ i2.
 #cs #l #m #i1 #m2 #H
 elim (at_inv_cons … H) -H * // #Hi1l #_ #Hli1
 elim (lt_le_false … Hi1l Hli1)
@@ -73,7 +73,7 @@ qed-.
 
 (* Main properties **********************************************************)
 
-theorem at_mono: â\88\80cs,i,i1. @â¦\83i, csâ¦\84 â\89\98 i1 â\86\92 â\88\80i2. @â¦\83i, csâ¦\84 ≘ i2 → i1 = i2.
+theorem at_mono: â\88\80cs,i,i1. @â\9dªi, csâ\9d« â\89\98 i1 â\86\92 â\88\80i2. @â\9dªi, csâ\9d« ≘ i2 → i1 = i2.
 #cs #i #i1 #H elim H -cs -i -i1
 [ #i #x #H <(at_inv_nil … H) -x //
 | #cs #l #m #i #i1 #Hil #_ #IHi1 #x #H