removing old contribs

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

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/fun.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/fun.ma
index 03dd7d0efd17551928787b915277bf7294adf7bc..4fcdab720b304f73e04e243f1c74b3a186f3e355 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NPlus/fun.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NPlus/fun.ma
@@ -12,28 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NPlus/fun".
+
 
 include "NPlus/inv.ma".
 
 (* Functional properties ****************************************************)
 
-theorem nplus_total: \forall p,q. \exists r. p + q == r.
- intros 2. elim q; clear q;
- [ autobatch | decompose. autobatch ].
+theorem nplus_total: ∀p,q. ∃r. p ⊕ q ≍ r.
+ intros; elim q; clear q;
+ [ autobatch | decompose; autobatch ].
 qed.
 
-theorem nplus_mono: \forall p,q,r1. (p + q == r1) \to 
-                    \forall r2. (p + q == r2) \to r1 = r2.
- intros 4. elim H; clear H q r1;
+theorem nplus_mono: ∀p,q,r1. p ⊕ q ≍ r1 → 
+                    ∀r2. p ⊕ q ≍ r2 → r1 = r2.
+ intros 4; elim H; clear H q r1;
  [ lapply linear nplus_inv_zero_2 to H1
  | lapply linear nplus_inv_succ_2 to H3. decompose
  ]; destruct; autobatch.
 qed.
 
-theorem nplus_inj_1: \forall p1, q, r. (p1 + q == r) \to
-                     \forall p2. (p2 + q == r) \to p2 = p1.
- intros 4. elim H; clear H q r;
+theorem nplus_inj_1: ∀p1, q, r. p1 ⊕ q ≍ r →
+                     ∀p2. p2 ⊕ q ≍ r → p2 = p1.
+ intros 4; elim H; clear H q r;
  [ lapply linear nplus_inv_zero_2 to H1
  | lapply linear nplus_inv_succ_2_3 to H3
  ]; autobatch.