Proof of Duality (cont’d)

• Now, we are equipped to prove the duality theorem.

• Let’s say that the original equation is:

  • S = T, where S and T are expressions.
  • Let’s now invert both sides of our equation:
    • S’ = T’
  • But inverting is the same as taking the ID, so
    • SID = TID
  • Now, let S = f( A, B, C, …, 0, 1, +,• ), and T = g( A, B, C, …, 0, 1, +,• )
  • Thus:
    • f( A, B, C, …, 0, 1, +, • )ID = g( A, B, C, …, 0, 1, +, • )ID
  • Or, by the definition of ID
    • f( A’, B’, C’, …, 1, 0, •, + ) = g( A’, B’, C’, …, 0, 1, +, • )

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