-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / GRP011-4.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: GRP011-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP011-4 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Group Theory *)
+
+(*  Problem  : Left cancellation *)
+
+(*  Version  : [Wos65] (equality) axioms : Incomplete. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Wos65] Wos (1965), Unpublished Note *)
+
+(*           : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+
+(*  Source   : [Pel86] *)
+
+(*  Names    : Pelletier 63 [Pel86] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 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    :    6 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   0 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments : [Pel86] says "... problems, published I think, by Larry Wos *)
+
+(*             (but I cannot locate where)." *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The operation '*' is associative  *)
+
+(* ----There exists an identity element  *)
+ntheorem prove_left_cancellation:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀b:Univ.
+∀c:Univ.
+∀d:Univ.
+∀identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:eq Univ (multiply b c) (multiply d c).
+∀H1:∀X:Univ.eq Univ (multiply (inverse X) X) identity.
+∀H2:∀X:Univ.eq Univ (multiply identity X) X.
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#b.
+#c.
+#d.
+#identity.
+#inverse.
+#multiply.
+#H0.
+#H1.
+#H2.
+#H3.
+nauto by H0,H1,H2,H3;
+nqed.
+
+(* -------------------------------------------------------------------------- *)