update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / fr2_nat.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma
index d71dc8fb4df8496e6f800baf28d0a68e74c42c85..6b3d84f8a7697ffaba7a029c02b22dc80369984d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma
@@ -17,13 +17,13 @@ include "ground/arith/nat_plus.ma".
 include "ground/arith/nat_lt.ma".
 include "ground/relocation/fr2_map.ma".
 
-(* NON-NEGATIVE APPLICATION FOR FINITE RELOCATION MAPS WITH PAIRS *******************************************)
+(* NON-NEGATIVE APPLICATION FOR FINITE RELOCATION MAPS WITH PAIRS ***********)
 
 (*** at *)
 inductive fr2_nat: fr2_map → relation nat ≝
 (*** at_nil *)
-| fr2_nat_nil (l):
-  fr2_nat (◊) l l
+| fr2_nat_empty (l):
+  fr2_nat (𝐞) l l
 (*** at_lt *)
 | fr2_nat_lt (f) (d) (h) (l1) (l2):
   l1 < d → fr2_nat f l1 l2 → fr2_nat (❨d,h❩;f) l1 l2
@@ -36,12 +36,12 @@ interpretation
   "non-negative relational application (finite relocation maps with pairs)"
   'RAt l1 f l2 = (fr2_nat f l1 l2).
 
-(* Basic inversion lemmas ***************************************************)
+(* Basic inversions *********************************************************)
 
 (*** at_inv_nil *)
-lemma fr2_nat_inv_nil (l1) (l2):
-      @â\9dªl1, â\97\8aâ\9d« ≘ l2 → l1 = l2.
-#l1 #l2 @(insert_eq_1 … (◊))
+lemma fr2_nat_inv_empty (l1) (l2):
+      @â\9d¨l1, ð\9d\90\9eâ\9d© ≘ l2 → l1 = l2.
+#l1 #l2 @(insert_eq_1 … (𝐞))
 #f * -f -l1 -l2
 [ //
 | #f #d #h #l1 #l2 #_ #_ #H destruct
@@ -50,10 +50,10 @@ lemma fr2_nat_inv_nil (l1) (l2):
 qed-.
 
 (*** at_inv_cons *)
-lemma fr2_nat_inv_cons (f) (d) (h) (l1) (l2):
-      @â\9dªl1, â\9d¨d,hâ\9d©;fâ\9d« ≘ l2 →
-      â\88¨â\88¨ â\88§â\88§ l1 < d & @â\9dªl1, fâ\9d« ≘ l2 
-       | â\88§â\88§ d â\89¤ l1 & @â\9dªl1+h, fâ\9d« ≘ l2.
+lemma fr2_nat_inv_lcons (f) (d) (h) (l1) (l2):
+      @â\9d¨l1, â\9d¨d,hâ\9d©;fâ\9d© ≘ l2 →
+      â\88¨â\88¨ â\88§â\88§ l1 < d & @â\9d¨l1, fâ\9d© ≘ l2 
+       | â\88§â\88§ d â\89¤ l1 & @â\9d¨l1+h, fâ\9d© ≘ l2.
 #g #d #h #l1 #l2 @(insert_eq_1 … (❨d, h❩;g))
 #f * -f -l1 -l2
 [ #l #H destruct
@@ -63,17 +63,17 @@ lemma fr2_nat_inv_cons (f) (d) (h) (l1) (l2):
 qed-.
 
 (*** at_inv_cons *)
-lemma fr2_nat_inv_cons_lt (f) (d) (h) (l1) (l2):
-      @â\9dªl1, â\9d¨d,hâ\9d©;fâ\9d« â\89\98 l2 â\86\92 l1 < d â\86\92 @â\9dªl1, fâ\9d« ≘ l2.
+lemma fr2_nat_inv_lcons_lt (f) (d) (h) (l1) (l2):
+      @â\9d¨l1, â\9d¨d,hâ\9d©;fâ\9d© â\89\98 l2 â\86\92 l1 < d â\86\92 @â\9d¨l1, fâ\9d© ≘ l2.
 #f #d #h #l1 #h2 #H
-elim (fr2_nat_inv_cons … H) -H * // #Hdl1 #_ #Hl1d
+elim (fr2_nat_inv_lcons … H) -H * // #Hdl1 #_ #Hl1d
 elim (nlt_ge_false … Hl1d Hdl1)
 qed-.
 
 (*** at_inv_cons *)
-lemma fr2_nat_inv_cons_ge (f) (d) (h) (l1) (l2):
-      @â\9dªl1, â\9d¨d,hâ\9d©;fâ\9d« â\89\98 l2 â\86\92 d â\89¤ l1 â\86\92 @â\9dªl1+h, fâ\9d« ≘ l2.
+lemma fr2_nat_inv_lcons_ge (f) (d) (h) (l1) (l2):
+      @â\9d¨l1, â\9d¨d,hâ\9d©;fâ\9d© â\89\98 l2 â\86\92 d â\89¤ l1 â\86\92 @â\9d¨l1+h, fâ\9d© ≘ l2.
 #f #d #h #l1 #h2 #H
-elim (fr2_nat_inv_cons … H) -H * // #Hl1d #_ #Hdl1
+elim (fr2_nat_inv_lcons … H) -H * // #Hl1d #_ #Hdl1
 elim (nlt_ge_false … Hl1d Hdl1)
 qed-.