propagating the arithmetics library, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic.ma
index 60ea38e24bcdcf01636d393ee7f8b09dbfe55875..f6671fa46e9d8ae78bd4f4e35e83550832ddc302 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground/notation/functions/basic_2.ma".
-include "ground/relocation/rtmap_at.ma".
+include "ground/relocation/rtmap_uni.ma".
 
 (* RELOCATION MAP ***********************************************************)
 
@@ -22,25 +22,12 @@ definition basic: nat → nat → rtmap ≝ λm,n. ⫯*[m] 𝐔❨n❩.
 interpretation "basic relocation (rtmap)"
    'Basic m n = (basic m n).
 
-(* Prioerties with application **********************************************)
+(* Basic properties *********************************************************)
 
-lemma at_basic_lt: ∀m,n,i. i < m → @❪i, 𝐁❨m,n❩❫ ≘ i.
-#m elim m -m [ #n #i #H elim (lt_zero_false … H) ]
-#m #IH #n * [ /2 width=2 by refl, at_refl/ ]
-#i #H lapply (lt_S_S_to_lt … H) -H /3 width=7 by refl, at_push/
+lemma at_basic_succ_sn (m) (n): ⫯𝐁❨m,n❩ = 𝐁❨↑m,n❩.
+#m #n >pushs_S //
 qed.
 
-lemma at_basic_ge: ∀m,n,i. m ≤ i → @❪i, 𝐁❨m,n❩❫ ≘ n+i.
-#m elim m -m //
-#m #IH #n #j #H
-elim (le_inv_S1 … H) -H #i #Hmi #H destruct
-/3 width=7 by refl, at_push/
+lemma at_basic_zero_succ (n): ↑𝐁❨𝟎,n❩ = 𝐁❨𝟎,↑n❩.
+#n >nexts_S //
 qed.
-
-(* Inversion lemmas with application ****************************************)
-
-lemma at_basic_inv_lt: ∀m,n,i,j. i < m → @❪i, 𝐁❨m,n❩❫ ≘ j → i = j.
-/3 width=4 by at_basic_lt, at_mono/ qed-.
-
-lemma at_basic_inv_ge: ∀m,n,i,j. m ≤ i → @❪i, 𝐁❨m,n❩❫ ≘ j → n+i = j.
-/3 width=4 by at_basic_ge, at_mono/ qed-.