Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / ROB020-1.ma

diff --git a/matita/matita/contribs/ng_TPTP/ROB020-1.ma b/matita/matita/contribs/ng_TPTP/ROB020-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: ROB020-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : ROB020-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Robbins Algebra *)
+
+(*  Problem  : -(a + -b)=b => Boolean *)
+
+(*  Version  : [Win90] (equality) axioms. *)
+
+(*             Theorem formulation : Denies Huntington's axiom. *)
+
+(*  English  : If there exist a, b such that -(a + -b) = b, the algebra  *)
+
+(*             is Boolean. *)
+
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(*  Source   : [Win90] *)
+
+(*  Names    : Corollary 3.10 [Win90] *)
+
+(*  Status   : Unknown *)
+
+(*  Rating   : 1.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   2 RR) *)
+
+(*             Number of atoms       :    5 (   5 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    4 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables   :    7 (   0 singleton) *)
+
+(*             Maximal term depth    :    6 (   3 average) *)
+
+(*  Comments : Commutativity, associativity, and Huntington's axiom  *)
+
+(*             axiomatize Boolean algebra. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for Robbins algebra  *)
+
+(* Inclusion of: Axioms/ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : ROB001-0 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Robbins algebra *)
+
+(*  Axioms   : Robbins algebra axioms *)
+
+(*  Version  : [Win90] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(*  Source   : [OTTER] *)
+
+(*  Names    : Lemma 2.2 [Win90] *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 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   :    2 (   0 constant; 1-2 arity) *)
+
+(*             Number of variables  :    7 (   0 singleton) *)
+
+(*             Maximal term depth   :    6 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_huntingtons_axiom:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀negate:∀_:Univ.Univ.
+∀H0:eq Univ (negate (add a (negate b))) b.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b)
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#b ##.
+#negate ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)