Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / LDA007-3.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: LDA007-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LDA007-3 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : LD-Algebras (Embedding algebras) *)
+
+(*  Problem  : Let g = cr(t). Show that t(tsg) = tt(ts)(tg)  *)
+
+(*  Version  : [Jec93] axioms : Incomplete > Reduced & Augmented > Incomplete. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Jec93] Jech (1993), LD-Algebras *)
+
+(*  Source   : [Jec93] *)
+
+(*  Names    : Problem 8 [Jec93] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   6 RR) *)
+
+(*             Number of atoms       :    7 (   7 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    9 (   8 constant; 0-2 arity) *)
+
+(*             Number of variables   :    3 (   0 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Embedding algebra axioms  *)
+
+(*  include('Axioms/LDA001-0.ax'). *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----t(tsk) = tt(ts)(tk), where k=crit(t)  *)
+ntheorem prove_equation:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀f:∀_:Univ.∀_:Univ.Univ.
+∀k:Univ.
+∀s:Univ.
+∀t:Univ.
+∀tk:Univ.
+∀ts:Univ.
+∀tsk:Univ.
+∀tt:Univ.
+∀tt_ts:Univ.
+∀H0:eq Univ tsk (f ts k).
+∀H1:eq Univ tk (f t k).
+∀H2:eq Univ tt_ts (f tt ts).
+∀H3:eq Univ ts (f t s).
+∀H4:eq Univ tt (f t t).
+∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#f ##.
+#k ##.
+#s ##.
+#t ##.
+#tk ##.
+#ts ##.
+#tsk ##.
+#tt ##.
+#tt_ts ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+nauto by H0,H1,H2,H3,H4,H5 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)