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To see why the ''Dispersion Rule'' holds, look at it this way: If ''x'' is true, then the presence of ''x'' makes no difference on either side of the equation, but if ''x'' is false, then both sides of the equation are false.
To see why the ''Dispersion Rule'' holds, look at it this way: If <math>x\!</math> is true, then the presence of <math>x\!</math> makes no difference on either side of the equation, but if <math>x\!</math> is false, then both sides of the equation are false.
Here is a proof sketch for the ''Case Analysis-Synthesis Theorem'' (CAST):
Here is a proof sketch for the ''Case Analysis-Synthesis Theorem'' (CAST):