removing old contribs

[helm.git] / helm / software / matita / contribs / RELATIONAL / NPlus / inv.ma

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
index b6ac60873ae2788f95fa9569a754f9949319b913..cfba0a843551ca03c3099eb41a4a87006722f134 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NPlus/inv.ma
@@ -12,70 +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.
+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;
- [ autobatch depth = 4
- | clear H1. decompose. destruct. autobatch 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; destruct. autobatch.
+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.
- autobatch 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; destruct. autobatch.
+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; destruct;
+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. destruct. autobatch.
+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. destruct. autobatch.
+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
  ]; 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.
+ | lapply linear nplus_inv_succ_1_3 to H1
  ]; autobatch.
 qed.