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                               THE PROOF
 
                 Copyright (C) 1978 Homer Wilson Smith
       Redistribution rights granted for non commercial purposes.
 
 
 Definitions:            a.  = means 'is equivalent to by definition'
                         b.  - = NOT
                         c.  (A -> B ; -> C) = (A -> B) and (B -> C)

                         L = Learning
                         C = Certainty
                         D = space time Distance
                       LBE = Learning by Being an Effect

 
 To be proved:          (L and C) -> -D
       Learning with Certainty implies no space time Distance.

 
 Assumptions:            1.  L <--> (L and C) or (L and -C)
   Learning implies Learning with Certainty or Learning with Not Certainty
                         2.  (D and L) -> LBE
         Distance and Learning implies Learning by Being an Effect.
                         3.  LBE -> -(L and C)
        Learning by Being an Effect implies Not Learning with Certainty.
                         4.  (L and C) -> -D
              Learning with Certainty implies Learning, but
                     Not by Being an Effect, and
                   Not across a space time Distance.
 
 Specific     (2,3)[A]   5.  (D and L) -> -(L and C)
 Logics:    (5)[B];[C]   6.  (L and C) -> -(D and L) ; -> (-D or -L)
                   [D]   7.  (L and C) -> L
          (6,7)[E];[F]   8.  (L and C) -> ((-D or -L) and L); -> -D
                (8)[A]   9.  (L and C) -> -D
 
                                  Q.E.D.
 
 General      (T.O.I.)   A.  ((A -> B) and (B -> C)) -> (A -> C)
 Logics:        (M.T.)   B.  (A -> B) -> (-B -> -A)
            (D.N.O.A.)   C.  -(A and B) -> (-A or -B)
                         D.  (A and B) -> A
                 (ADD)   E.  ((A -> B) and (A -> C)) -> (A -> (B and C))
                         F.  ((A or B) and -B) -> A
 
 
 Names of      T.O.I. means Transitivity Of Implication
 General         M.T. means Modus Tolens
 Logics:     D.N.O.A. means Distribution of Not Over And
                 ADD  means Addition
 
 
                                                        12/14/1978
 
                                                     Homer Wilson Smith