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 67fd827ad73ae2a2aed696a9923639162cd6c972..59e8c9fe6a32db046bcf79b54d1de98ec83dbf36 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/notation/relations/rat_3.ma".
+include "ground/notation/relations/ratsection_3.ma".
 include "ground/arith/nat_plus.ma".
 include "ground/arith/nat_lt.ma".
 include "ground/relocation/fr2_map.ma".
@@ -22,26 +22,26 @@ include "ground/relocation/fr2_map.ma".
 (*** 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
+  l1 < d → fr2_nat f l1 l2 → fr2_nat (❨d,h❩◗f) l1 l2
 (*** at_ge *)
 | fr2_nat_ge (f) (d) (h) (l1) (l2):
-  d ≤ l1 → fr2_nat f (l1 + h) l2 → fr2_nat (❨d,h❩;f) l1 l2
+  d ≤ l1 → fr2_nat f (l1 + h) l2 → fr2_nat (❨d,h❩◗f) l1 l2
 .
 
 interpretation
   "non-negative relational application (finite relocation maps with pairs)"
-  'RAt l1 f l2 = (fr2_nat f l1 l2).
+  'RAtSection l1 f l2 = (fr2_nat f l1 l2).
 
 (* Basic inversions *********************************************************)
 
 (*** at_inv_nil *)
-lemma fr2_nat_inv_nil (l1) (l2):
-      @❪l1, ◊❫ ≘ l2 → l1 = l2.
-#l1 #l2 @(insert_eq_1 … (◊))
+lemma fr2_nat_inv_empty (l1) (l2):
+      ＠§❨l1, 𝐞❩ ≘ l2 → l1 = l2.
+#l1 #l2 @(insert_eq_1 … (𝐞))
 #f * -f -l1 -l2
 [ //
 | #f #d #h #l1 #l2 #_ #_ #H destruct
@@ -50,11 +50,11 @@ lemma fr2_nat_inv_nil (l1) (l2):
 qed-.
 
 (*** at_inv_cons *)
-lemma fr2_nat_inv_cons (f) (d) (h) (l1) (l2):
-      @❪l1, ❨d,h❩;f❫ ≘ l2 →
-      ∨∨ ∧∧ l1 < d & @❪l1, f❫ ≘ l2 
-       | ∧∧ d ≤ l1 & @❪l1+h, f❫ ≘ l2.
-#g #d #h #l1 #l2 @(insert_eq_1 … (❨d, h❩;g))
+lemma fr2_nat_inv_lcons (f) (d) (h) (l1) (l2):
+      ＠§❨l1, ❨d,h❩◗f❩ ≘ l2 →
+      ∨∨ ∧∧ l1 < d & ＠§❨l1, f❩ ≘ l2 
+       | ∧∧ d ≤ l1 & ＠§❨l1+h, f❩ ≘ l2.
+#g #d #h #l1 #l2 @(insert_eq_1 … (❨d, h❩◗g))
 #f * -f -l1 -l2
 [ #l #H destruct
 | #f1 #d1 #h1 #l1 #l2 #Hld1 #Hl12 #H destruct /3 width=1 by or_introl, conj/
@@ -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):
-      @❪l1, ❨d,h❩;f❫ ≘ l2 → l1 < d → @❪l1, f❫ ≘ l2.
+lemma fr2_nat_inv_lcons_lt (f) (d) (h) (l1) (l2):
+      ＠§❨l1, ❨d,h❩◗f❩ ≘ l2 → l1 < d → ＠§❨l1, f❩ ≘ 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):
-      @❪l1, ❨d,h❩;f❫ ≘ l2 → d ≤ l1 → @❪l1+h, f❫ ≘ l2.
+lemma fr2_nat_inv_lcons_ge (f) (d) (h) (l1) (l2):
+      ＠§❨l1, ❨d,h❩◗f❩ ≘ l2 → d ≤ l1 → ＠§❨l1+h, f❩ ≘ 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-.