A few paramodulation/demodulation tests moved from library to tests.

[helm.git] / helm / matita / library / SK.ma

diff --git a/helm/matita/library/SK.ma b/helm/matita/library/SK.ma
deleted file mode 100644 (file)
index 708f92f..0000000
--- a/helm/matita/library/SK.ma
+++ /dev/null
@@ -1,116 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/SK/".
-
-include "legacy/coq.ma".
-alias symbol "eq" = "Coq's leibnitz's equality".
-
-theorem SKK:
-  \forall A:Set.
-  \forall app: A \to A \to A.
-  \forall K:A. 
-  \forall S:A.
-  \forall H1: (\forall x,y:A.(app (app K x) y) = x).
-  \forall H2: (\forall x,y,z:A.
-    (app (app (app S x) y) z) = (app (app x z) (app y z))).
-  \forall x:A.
-    (app (app (app S K) K) x) = x.
-intros.auto paramodulation.
-qed.
-
-theorem bool1:
-  \forall A:Set.
-  \forall one:A.
-  \forall zero:A.
-  \forall add: A \to A \to A.
-  \forall mult: A \to A \to A.
-  \forall inv: A \to A.
-  \forall c1:(\forall x,y:A.(add x y) = (add y x)). 
-  \forall c2:(\forall x,y:A.(mult x y) = (mult y x)). 
-  \forall d1: (\forall x,y,z:A.
-              (add x (mult y z)) = (mult (add x y) (add x z))).
-  \forall d2: (\forall x,y,z:A.
-              (mult x (add y z)) = (add (mult x y) (mult x z))).  
-  \forall i1: (\forall x:A. (add x zero) = x).
-  \forall i2: (\forall x:A. (mult x one) = x).   
-  \forall inv1: (\forall x:A. (add x (inv x)) = one).  
-  \forall inv2: (\forall x:A. (mult x (inv x)) = zero). 
-  (inv zero) = one.
-intros.auto paramodulation.
-qed.
-  
-theorem bool2:
-  \forall A:Set.
-  \forall one:A.
-  \forall zero:A.
-  \forall add: A \to A \to A.
-  \forall mult: A \to A \to A.
-  \forall inv: A \to A.
-  \forall c1:(\forall x,y:A.(add x y) = (add y x)). 
-  \forall c2:(\forall x,y:A.(mult x y) = (mult y x)). 
-  \forall d1: (\forall x,y,z:A.
-              (add x (mult y z)) = (mult (add x y) (add x z))).
-  \forall d2: (\forall x,y,z:A.
-              (mult x (add y z)) = (add (mult x y) (mult x z))).  
-  \forall i1: (\forall x:A. (add x zero) = x).
-  \forall i2: (\forall x:A. (mult x one) = x).   
-  \forall inv1: (\forall x:A. (add x (inv x)) = one).  
-  \forall inv2: (\forall x:A. (mult x (inv x)) = zero).
-  \forall x:A. (mult x zero) = zero.
-intros.auto paramodulation.
-qed.
-
-theorem bool3:
-  \forall A:Set.
-  \forall one:A.
-  \forall zero:A.
-  \forall add: A \to A \to A.
-  \forall mult: A \to A \to A.
-  \forall inv: A \to A.
-  \forall c1:(\forall x,y:A.(add x y) = (add y x)). 
-  \forall c2:(\forall x,y:A.(mult x y) = (mult y x)). 
-  \forall d1: (\forall x,y,z:A.
-              (add x (mult y z)) = (mult (add x y) (add x z))).
-  \forall d2: (\forall x,y,z:A.
-              (mult x (add y z)) = (add (mult x y) (mult x z))).  
-  \forall i1: (\forall x:A. (add x zero) = x).
-  \forall i2: (\forall x:A. (mult x one) = x).   
-  \forall inv1: (\forall x:A. (add x (inv x)) = one).  
-  \forall inv2: (\forall x:A. (mult x (inv x)) = zero).
-  \forall x:A. (inv (inv x)) = x.
-intros.auto paramodulation.
-qed.
-  
-theorem bool2:
-  \forall A:Set.
-  \forall one:A.
-  \forall zero:A.
-  \forall add: A \to A \to A.
-  \forall mult: A \to A \to A.
-  \forall inv: A \to A.
-  \forall c1:(\forall x,y:A.(add x y) = (add y x)). 
-  \forall c2:(\forall x,y:A.(mult x y) = (mult y x)). 
-  \forall d1: (\forall x,y,z:A.
-              (add x (mult y z)) = (mult (add x y) (add x z))).
-  \forall d2: (\forall x,y,z:A.
-              (mult x (add y z)) = (add (mult x y) (mult x z))).  
-  \forall i1: (\forall x:A. (add x zero) = x).
-  \forall i2: (\forall x:A. (mult x one) = x).   
-  \forall inv1: (\forall x:A. (add x (inv x)) = one).  
-  \forall inv2: (\forall x:A. (mult x (inv x)) = zero). 
-  \forall x,y:A.
-    (inv (mult x y)) = (add (inv x) (inv y)).
-intros.auto paramodulation.
-qed.