X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_minus_plus.ma;h=e910fdaa0c94802be4767ba40f7e13a349951a46;hb=8fdf1af656038d0245eba64ff2531bbe94ce0e9e;hp=3e018b7759cfa8b16bb6ce6c0ac779941bdf3539;hpb=21de0d35017656c5a55528390b54b0b2ae395b44;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_plus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_plus.ma
index 3e018b775..e910fdaa0 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_plus.ma
@@ -25,6 +25,7 @@ lemma nminus_plus_sn_refl_sn (m) (n): m = m + n - n.
 #n #IH <nplus_succ_dx <nminus_succ_bi //
 qed.
 
+(*** minus_plus_m_m_commutative *)
 lemma nminus_plus_sn_refl_dx (m) (n): m = n + m - n.
 #m #n <nplus_comm //
 qed.
@@ -33,17 +34,13 @@ qed.
 theorem nminus_plus_assoc (o) (m) (n): o-m-n = o-(m+n).
 #o #m #n @(nat_ind_succ … n) -n //
 #n #IH <nplus_succ_dx <nminus_succ_dx <nminus_succ_dx //
-qed-.
+qed.
 
 (*** minus_plus_plus_l *)
 lemma nminus_plus_dx_bi (m) (n) (o): m - n = (m + o) - (n + o).
-#m #n #o <nminus_plus_assoc <nminus_minus_comm //
+#m #n #o <nminus_plus_assoc <nminus_comm //
 qed.
 
-(*** plus_minus_plus_plus_l *) (**)
-lemma plus_minus_plus_plus_l: ∀z,x,y,h. z + (x + h) - (y + h) = z + x - y.
-// qed-.
-
 (* Helper constructions with nplus ******************************************)
 
 (*** plus_to_minus *)
@@ -62,15 +59,15 @@ lemma eq_inv_plus_nminus_refl_sn (m) (n) (o):
       m + o = m - n →
       ∨∨ ∧∧ 𝟎 = m & 𝟎 = o
        | ∧∧ 𝟎 = n & 𝟎 = o.
-#m #n @(nat_ind_succ_2 … m n) -m -n
+#m #n @(nat_ind_2_succ … m n) -m -n
 [ /3 width=1 by or_introl, conj/
-| #m #o #Ho
+| #m #_ #o #Ho
   lapply (eq_inv_nplus_bi_sn … (𝟎) Ho) -Ho
   /3 width=1 by or_intror, conj/
 | #m #n #IH #o
   <nminus_succ_bi >nplus_succ_shift #Ho
   elim (IH … Ho) -IH -Ho * #_ #H
-  elim (eq_inv_nzero_succ … H)
+  elim (eq_inv_zero_nsucc … H)
 ]
 qed-.