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[helm.git] / matitaB / matita / contribs / ng_TPTP / LAT007-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: LAT007-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT007-1 : TPTP v3.7.0. Released v2.2.0. *)
+
+(*  Domain   : Lattice Theory (Distributive lattices) *)
+
+(*  Problem  : Sholander's basis for distributive lattices, part 5 (of 6). *)
+
+(*  Version  : [MP96] (equality) axioms. *)
+
+(*  English  : This is part of the proof that Sholanders 2-basis for *)
+
+(*             distributive lattices is correct. Here we prove associativity  *)
+
+(*             of join. *)
+
+(*  Refs     : [McC98] McCune (1998), Email to G. Sutcliffe *)
+
+(*           : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq *)
+
+(*  Source   : [McC98] *)
+
+(*  Names    : LT-3-e [MP96] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1 *)
+
+(*  Syntax   : Number of clauses     :    3 (   0 non-Horn;   3 unit;   1 RR) *)
+
+(*             Number of atoms       :    3 (   3 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    5 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   1 singleton) *)
+
+(*             Maximal term depth    :    3 (   3 average) *)
+
+(*  Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Sholander's 2-basis for distributive lattices: *)
+
+(* ----Denial of the conclusion: *)
+ntheorem prove_associativity_of_join:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀c:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)).
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join (join a b) c) (join a (join b c)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#join ##.
+#meet ##.
+#H0 ##.
+#H1 ##.
+nauto by H0,H1 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)