X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_plus.ma;h=a9894fc6285e7aaf7ec746ddfebacb208b91885e;hb=0bcf2dc1a27e38cb6cd3d44eb838d652926841e0;hp=40beec972819238df4a5bdd75ed92e403d48d436;hpb=888840f6b3a71d3d686b53b702d362ab90ab0038;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_plus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_plus.ma
index 40beec972..a9894fc62 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_plus.ma
@@ -18,7 +18,7 @@ include "ground/arith/nat_succ_iter.ma".
 
 (*** plus *)
 definition nplus: nat → nat → nat ≝
-           λm,n. nsucc^n m.
+           λm,n. (nsucc^n) m.
 
 interpretation
   "plus (non-negative integers)"
@@ -31,7 +31,7 @@ lemma nplus_zero_dx (m): m = m + 𝟎.
 // qed.
 
 (*** plus_SO_dx *)
-lemma nplus_one_dx (n): ↑n = n + 𝟏.
+lemma nplus_unit_dx (n): ↑n = n + 𝟏.
 // qed.
 
 (*** plus_n_Sm *)
@@ -50,14 +50,14 @@ lemma niter_plus (A) (f) (n1) (n2):
 /3 width=5 by compose_repl_fwd_sn, compose_repl_fwd_dx/
 qed.
 
-(* Advanved constructions (semigroup properties) ****************************)
+(* Advanced constructions (semigroup properties) ****************************)
 
 (*** plus_S1 *)
 lemma nplus_succ_sn (m) (n): ↑(m+n) = ↑m + n.
 #m #n @(niter_appl … nsucc)
 qed.
 
-(*** plus_O_n.con *)
+(*** plus_O_n *)
 lemma nplus_zero_sn (m): m = 𝟎 + m.
 #m @(nat_ind_succ … m) -m //
 qed.
@@ -65,7 +65,7 @@ qed.
 (*** commutative_plus *)
 lemma nplus_comm: commutative … nplus.
 #m @(nat_ind_succ … m) -m //
-qed-. (**) (* gets in the way with auto *)
+qed-. (* * gets in the way with auto *)
 
 (*** associative_plus *)
 lemma nplus_assoc: associative … nplus.
@@ -76,11 +76,11 @@ qed.
 (* Helper constructions *****************************************************)
 
 (*** plus_SO_sn *)
-lemma nplus_one_sn (n): ↑n = 𝟏 + n.
+lemma nplus_unit_sn (n): ↑n = 𝟏 + n.
 #n <nplus_comm // qed.
 
 lemma nplus_succ_shift (m) (n): ↑m + n = m + ↑n.
-// qed-.
+// qed.
 
 (*** assoc_plus1 *)
 lemma nplus_plus_comm_12 (o) (m) (n): m + n + o = n + (m + o).
@@ -89,11 +89,11 @@ lemma nplus_plus_comm_12 (o) (m) (n): m + n + o = n + (m + o).
 (*** plus_plus_comm_23 *)
 lemma nplus_plus_comm_23 (o) (m) (n): o + m + n = o + n + m.
 #o #m #n >nplus_assoc >nplus_assoc <nplus_comm in ⊢ (??(??%)?); //
-qed-.
+qed.
 
 (* Basic inversions *********************************************************)
 
-(*** plus_inv_O3 zero_eq_plus *) 
+(*** zero_eq_plus *)
 lemma eq_inv_zero_nplus (m) (n): 𝟎 = m + n → ∧∧ 𝟎 = m & 𝟎 = n.
 #m #n @(nat_ind_succ … n) -n
 [ /2 width=1 by conj/
@@ -102,6 +102,11 @@ lemma eq_inv_zero_nplus (m) (n): 𝟎 = m + n → ∧∧ 𝟎 = m & 𝟎 = n.
 ]
 qed-.
 
+(*** plus_inv_O3 *)
+lemma eq_inv_nplus_zero (m) (n):
+      m + n = 𝟎 → ∧∧ 𝟎 = m & 𝟎 = n.
+/2 width=1 by eq_inv_zero_nplus/ qed-.
+
 (*** injective_plus_l *)
 lemma eq_inv_nplus_bi_dx (o) (m) (n): m + o = n + o → m = n.
 #o @(nat_ind_succ … o) -o /3 width=1 by eq_inv_nsucc_bi/