update in ground, basic_2A and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / fr2_minus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma
index a97d130679db19a112d7640e0d730168da857314..1e54b3846a32c0a024042f100960cfa4e6331247 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma
@@ -19,31 +19,31 @@ include "ground/arith/nat_minus.ma".
 include "ground/arith/nat_lt.ma".
 include "ground/relocation/fr2_map.ma".
 
-(* RELATIONAL SUBTRACTION FOR FINITE RELOCATION MAPS WITH PAIRS *******************************************)
+(* RELATIONAL SUBTRACTION FOR FINITE RELOCATION MAPS WITH PAIRS *************)
 
 (*** minuss *)
 inductive fr2_minus: nat → relation fr2_map ≝
 (*** minuss_nil *)
-| fr2_minus_nil (i):
-  fr2_minus i (◊) (◊)
+| fr2_minus_empty (i):
+  fr2_minus i (𝐞) (𝐞)
 (*** minuss_lt *)
 | fr2_minus_lt (f1) (f2) (d) (h) (i):
-  i < d → fr2_minus i f1 f2 → fr2_minus i (❨d,h❩;f1) (❨d-i,h❩;f2)
+  i < d → fr2_minus i f1 f2 → fr2_minus i (❨d,h❩◗f1) (❨d-i,h❩◗f2)
 (*** minuss_ge *)
 | fr2_minus_ge (f1) (f2) (d) (h) (i):
-  d ≤ i → fr2_minus (h+i) f1 f2 → fr2_minus i (❨d,h❩;f1) f2
+  d ≤ i → fr2_minus (h+i) f1 f2 → fr2_minus i (❨d,h❩◗f1) f2
 .
 
 interpretation
   "minus (finite relocation maps with pairs)"
   'RMinus f1 i f2 = (fr2_minus i f1 f2).
 
-(* Basic inversion lemmas ***************************************************)
+(* Basic inversions *********************************************************)
 
 (*** minuss_inv_nil1 *)
-lemma fr2_minus_inv_nil_sn (f2) (i):
-      ◊ ▭ i ≘ f2 → f2 = ◊.
-#f2 #i @(insert_eq_1 … (◊))
+lemma fr2_minus_inv_empty_sn (f2) (i):
+      𝐞 ▭ i ≘ f2 → f2 = 𝐞.
+#f2 #i @(insert_eq_1 … (𝐞))
 #f1 * -f1 -f2 -i
 [ //
 | #f1 #f2 #d #h #i #_ #_ #H destruct
@@ -52,11 +52,11 @@ lemma fr2_minus_inv_nil_sn (f2) (i):
 qed-.
 
 (*** minuss_inv_cons1 *)
-lemma fr2_minus_inv_cons_sn (f1) (f2) (d) (h) (i):
-      ❨d, h❩;f1 ▭ i ≘ f2 →
+lemma fr2_minus_inv_lcons_sn (f1) (f2) (d) (h) (i):
+      ❨d, h❩◗f1 ▭ i ≘ f2 →
       ∨∨ ∧∧ d ≤ i & f1 ▭ h+i ≘ f2
-       | ∃∃f. i < d & f1 ▭ i ≘ f & f2 = ❨d-i,h❩;f.
-#g1 #f2 #d #h #i @(insert_eq_1 … (❨d,h❩;g1))
+       | ∃∃f. i < d & f1 ▭ i ≘ f & f2 = ❨d-i,h❩◗f.
+#g1 #f2 #d #h #i @(insert_eq_1 … (❨d,h❩◗g1))
 #f1 * -f1 -f2 -i
 [ #i #H destruct
 | #f1 #f #d1 #h1 #i1 #Hid1 #Hf #H destruct /3 width=3 by ex3_intro, or_intror/
@@ -65,18 +65,18 @@ lemma fr2_minus_inv_cons_sn (f1) (f2) (d) (h) (i):
 qed-.
 
 (*** minuss_inv_cons1_ge *)
-lemma fr2_minus_inv_cons_sn_ge (f1) (f2) (d) (h) (i):
-      ❨d, h❩;f1 ▭ i ≘ f2 → d ≤ i → f1 ▭ h+i ≘ f2.
+lemma fr2_minus_inv_lcons_sn_ge (f1) (f2) (d) (h) (i):
+      ❨d, h❩◗f1 ▭ i ≘ f2 → d ≤ i → f1 ▭ h+i ≘ f2.
 #f1 #f2 #d #h #i #H
-elim (fr2_minus_inv_cons_sn … H) -H * // #f #Hid #_ #_ #Hdi
+elim (fr2_minus_inv_lcons_sn … H) -H * // #f #Hid #_ #_ #Hdi
 elim (nlt_ge_false … Hid Hdi)
 qed-.
 
 (*** minuss_inv_cons1_lt *)
-lemma fr2_minus_inv_cons_sn_lt (f1) (f2) (d) (h) (i):
-      ❨d, h❩;f1 ▭ i ≘ f2 → i < d →
-      ∃∃f. f1 ▭ i ≘ f & f2 = ❨d-i,h❩;f.
-#f1 #f2 #d #h #i #H elim (fr2_minus_inv_cons_sn … H) -H *
+lemma fr2_minus_inv_lcons_sn_lt (f1) (f2) (d) (h) (i):
+      ❨d, h❩◗f1 ▭ i ≘ f2 → i < d →
+      ∃∃f. f1 ▭ i ≘ f & f2 = ❨d-i,h❩◗f.
+#f1 #f2 #d #h #i #H elim (fr2_minus_inv_lcons_sn … H) -H *
 [ #Hdi #_ #Hid elim (nlt_ge_false … Hid Hdi)
 | /2 width=3 by ex2_intro/
 ]