X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNPlus%2Finv.ma;h=cfba0a843551ca03c3099eb41a4a87006722f134;hb=d9824956d9132109ed5f23380a0a1f9c5181d18a;hp=99bf3a9eeaa07b3a99d4048b73fdfc15b35065c3;hpb=b7503f874120f581c9679deabe45bd3c333f1b0c;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
index 99bf3a9ee..cfba0a843 100644
--- a/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
@@ -12,82 +12,70 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NPlus/inv".
+
 
 include "NPlus/defs.ma".
 
 (* Inversion lemmas *********************************************************)
 
-theorem nplus_inv_zero_1: \forall q,r. (zero + q == r) \to q = r.
- intros. elim H; clear H q r; auto.
+theorem nplus_inv_zero_1: ∀q,r. zero ⊕ q ≍ r → q = r.
+ intros. elim H; clear H q r; autobatch.
 qed.
 
-theorem nplus_inv_succ_1: \forall p,q,r. ((succ p) + q == r) \to 
-                          \exists s. r = (succ s) \land p + q == s.
+theorem nplus_inv_succ_1: ∀p,q,r. succ p ⊕ q ≍ r → 
+                          ∃s. r = succ s ∧ p ⊕ q ≍ s.
  intros. elim H; clear H q r; intros;
- [ auto depth = 4
- | clear H1. decompose. subst. auto depth = 4
+ [ autobatch depth = 3
+ | clear H1; decompose; destruct; autobatch depth = 4
  ]
 qed.
 
-theorem nplus_inv_zero_2: \forall p,r. (p + zero == r) \to p = r.
- intros. inversion H; clear H; intros;
- [ auto.
- | clear H H1. destruct H2.
- ].
+theorem nplus_inv_zero_2: ∀p,r. p ⊕ zero ≍ r → p = r.
+ intros; inversion H; clear H; intros; destruct; autobatch.
 qed.
 
-theorem nplus_inv_succ_2: \forall p,q,r. (p + (succ q) == r) \to 
-                          \exists s. r = (succ s) \land p + q == s.
- intros. inversion H; clear H; intros;
- [ destruct H.
- | clear H1 H3 r. destruct H2; clear H2. subst. auto depth = 4.
- ].
+theorem nplus_inv_succ_2: ∀p,q,r. p ⊕ succ q ≍ r → 
+                          ∃s. r = succ s ∧ p ⊕ q ≍ s.
+ intros; inversion H; clear H; intros; destruct.
+ autobatch depth = 3.
 qed.
 
-theorem nplus_inv_zero_3: \forall p,q. (p + q == zero) \to 
-                          p = zero \land q = zero.
- intros. inversion H; clear H; intros;
- [ subst. auto
- | clear H H1. destruct H3.
- ].
+theorem nplus_inv_zero_3: ∀p,q. p ⊕ q ≍ zero → 
+                          p = zero ∧ q = zero.
+ intros; inversion H; clear H; intros; destruct; autobatch.
 qed.
 
-theorem nplus_inv_succ_3: \forall p,q,r. (p + q == (succ r)) \to
-                          \exists s. p = succ s \land (s + q == r) \lor
-                                     q = succ s \land p + s == r.
- intros. inversion H; clear H; intros;
- [ subst
- | clear H1. destruct H3. clear H3. subst.
- ]; auto depth = 4.
+theorem nplus_inv_succ_3: ∀p,q,r. p ⊕ q ≍ succ r →
+                             ∃s. p = succ s ∧ s ⊕ q ≍ r ∨
+                               q = succ s ∧ p ⊕ s ≍ r.
+ intros; inversion H; clear H; intros; destruct;
+ autobatch depth = 4.
 qed.
 
 (* Corollaries to inversion lemmas ******************************************)
 
-theorem nplus_inv_succ_2_3: \forall p,q,r.
-                            (p + (succ q) == (succ r)) \to p + q == r.
- intros. 
- lapply linear nplus_inv_succ_2 to H. decompose. subst.
- destruct H1. clear H1. subst. auto.
+theorem nplus_inv_succ_2_3: ∀p,q,r.
+                            p ⊕ succ q ≍ succ r → p ⊕ q ≍ r.
+ intros;
+ lapply linear nplus_inv_succ_2 to H; decompose; destruct; autobatch.
 qed.
 
-theorem nplus_inv_succ_1_3: \forall p,q,r.
-                            ((succ p) + q == (succ r)) \to p + q == r.
- intros. 
- lapply linear nplus_inv_succ_1 to H. decompose. subst.
- destruct H1. clear H1. subst. auto.
+theorem nplus_inv_succ_1_3: ∀p,q,r.
+                            succ p ⊕ q ≍ succ r → p ⊕ q ≍ r.
+ intros;
+ lapply linear nplus_inv_succ_1 to H; decompose; destruct; autobatch.
 qed.
 
-theorem nplus_inv_eq_2_3: \forall p,q. (p + q == q) \to p = zero.
- intros 2. elim q; clear q;
+theorem nplus_inv_eq_2_3: ∀p,q. p ⊕ q ≍ q → p = zero.
+ intros 2; elim q; clear q;
  [ lapply linear nplus_inv_zero_2 to H
  | lapply linear nplus_inv_succ_2_3 to H1
- ]; auto.
+ ]; autobatch.
 qed.
 
-theorem nplus_inv_eq_1_3: \forall p,q. (p + q == p) \to q = zero.
- intros 1. elim p; clear p;
+theorem nplus_inv_eq_1_3: ∀p,q. p ⊕ q ≍ p → q = zero.
+ intros 1; elim p; clear p;
  [ lapply linear nplus_inv_zero_1 to H
- | lapply linear nplus_inv_succ_1_3 to H1.
- ]; auto.
+ | lapply linear nplus_inv_succ_1_3 to H1
+ ]; autobatch.
 qed.