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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