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The Register Partition segment of the propositional program consists of three universal partition expressions, taken in conjunction saying that the read head <math>H\!</math> must be reading one and only one of the registers or tape cells available to it at each of the points in time under consideration.  In sum:

The Register Partition segment of the propositional program consists of three universal partition expressions, taken in conjunction saying that the read head <math>\operatorname{H}</math> must be reading one and only one of the registers or tape cells available to it at each of the points in time under consideration.  In sum:

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<p>At each of the points in time <math>p_i,\!</math> for <math>i = 0, 1, 2,\!</math></p>

<p>At each of the points in time <math>p_i,\!</math> for <math>i = 0, 1, 2,\!</math></p>

<p><math>H\!</math> is reading exactly one cell <math>r_j,\!</math> for <math>j = 0, 1, 2.\!</math>

<p><math>\operatorname{H}</math> is reading exactly one cell <math>r_j,\!</math> for <math>j = 0, 1, 2.\!</math>

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