X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred.ma;h=c753d8f72379f0103801615af9cfcc2012aa0ec0;hb=19b0a814861157ba05f23877d5cd94059f52c2e8;hp=3d665506579765b2246ce3985a9458ed9154f49e;hpb=68e028d053806177e218ee1a5f8778d3011bef83;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred.ma
index 3d6655065..c753d8f72 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred.ma
@@ -28,8 +28,28 @@ interpretation
   "predecessor (non-negative integers)"
   'DownArrow m = (npred m).
 
-(* Basic rewrites ***********************************************************)
+(* Basic constructions ******************************************************)
 
 (*** pred_O *)
 lemma npred_zero: 𝟎 = ↓𝟎.
 // qed.
+
+lemma npred_one: 𝟎 = ↓𝟏.
+// qed.
+
+lemma npred_psucc (p): ninj p = ↓↑p.
+// qed.
+
+(* Basic inversions *********************************************************)
+
+lemma npred_pnat_inv_refl (p): ninj p = ↓p → ⊥.
+*
+[ <npred_one #H destruct
+| #p /3 width=2 by psucc_inv_refl, eq_inv_ninj_bi/
+]
+qed-.
+
+(*** pred_inv_fix_sn *)
+lemma npred_inv_refl (n): n = ↓n → 𝟎 = n.
+* // #p #H elim (npred_pnat_inv_refl … H)
+qed-.