X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_succ.ma;h=9455ca7447ec71159d8b204b184ebeaa8d209282;hb=21de0d35017656c5a55528390b54b0b2ae395b44;hp=c93a75d42fc4b9a35b4a93a812633a6291f6f23e;hpb=df7a2aa19e98dc28e7f22129275a175cead49e2d;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_succ.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_succ.ma
index c93a75d42..9455ca744 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_succ.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_succ.ma
@@ -14,7 +14,7 @@
 
 include "ground/arith/nat.ma".
 
-(* NON-NEGATIVE INTEGERS ****************************************************)
+(* SUCCESSOR FOR NON-NEGATIVE INTEGERS **************************************)
 
 definition nsucc: nat → nat ≝ λm. match m with
 [ nzero  ⇒ ninj (𝟏)
@@ -22,10 +22,10 @@ definition nsucc: nat → nat ≝ λm. match m with
 ].
 
 interpretation
-  "successor (non-negative integers"
+  "successor (non-negative integers)"
   'UpArrow m = (nsucc m).
 
-(* Basic rewrites ***********************************************************)
+(* Basic constructions ******************************************************)
 
 lemma nsucc_zero: ninj (𝟏) = ↑𝟎.
 // qed.
@@ -36,23 +36,23 @@ lemma nsucc_inj (p): ninj (↑p) = ↑(ninj p).
 (* Basic eliminations *******************************************************)
 
 (*** nat_ind *)
-lemma nat_ind (Q:predicate …):
+lemma nat_ind_succ (Q:predicate …):
       Q (𝟎) → (∀n. Q n → Q (↑n)) → ∀n. Q n.
 #Q #IH1 #IH2 * //
 #p elim p -p /2 width=1 by/
 qed-.
 
 (*** nat_elim2 *)
-lemma nat_ind_2 (Q:relation2 …):
+lemma nat_ind_succ_2 (Q:relation2 …):
       (∀n. Q (𝟎) n) →
       (∀m. Q (↑m) (𝟎)) →
       (∀m,n. Q m n → Q (↑m) (↑n)) →
       ∀m,n. Q m n.
-#Q #IH1 #IH2 #IH3 #m elim m -m [ // ]
-#m #IH #n elim n -n /2 width=1 by/
+#Q #IH1 #IH2 #IH3 #m @(nat_ind_succ … m) -m [ // ]
+#m #IH #n @(nat_ind_succ … n) -n /2 width=1 by/
 qed-.
 
-(* Basic inversions *********************************************************)
+(* Basic inversions ***************************************************************)
 
 (*** injective_S *)
 lemma eq_inv_nsucc_bi: injective … nsucc.