THE PROOF Copyright (C) 1978 Homer Wilson Smith Redistribution rights granted for non commerical purposes. Definitions: a. = means 'is equivalent to by definition' b. - = NOT c. (A -> B ; -> C) = (A -> B) and (B -> C) To be proved: (L and C) -> -D Assumptions: 1. L <--> (L and C) or (L and -C) 2. (D and L) -> LBE 3. LBE -> -(L and C) 4. (L and C) -> -D 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