Changes

The <math>j^\text{th}\!</math> ''extract'' of a strait of the form <math>S_1 \times \ldots \times S_k,\!</math> constrained to a frame of discussion where the number of places is restricted to <math>k,\!</math> is the strait of the form <math>X \times \ldots \times S_j \times \ldots \times X.</math>  In the appropriate context, this can be denoted more succinctly by the stricture <math>^{\backprime\backprime} \, (S_j)_{[j]} \, ^{\prime\prime},</math> an assertion that places the <math>j^\text{th}\!</math> set in the <math>j^\text{th}\!</math> place of the product.

The <math>j^\text{th}\!</math> ''extract'' of a strait of the form <math>S_1 \times \ldots \times S_k,\!</math> constrained to a frame of discussion where the number of places is restricted to <math>k,\!</math> is the strait of the form <math>X \times \ldots \times S_j \times \ldots \times X.</math>  In the appropriate context, this can be denoted more succinctly by the stricture <math>^{\backprime\backprime} \, (S_j)_{[j]} \, ^{\prime\prime},</math> an assertion that places the <math>j^\text{th}\!</math> set in the <math>j^\text{th}\!</math> place of the product.

In these terms, a stricture of the form <math>^{\backprime\backprime} \, S_1 \times \ldots \times S_k \, ^{\prime\prime}</math> can be expressed in terms of simpler strictures, to wit, as a conjunction of its <math>k\!</math> excerpts:

In these terms, a stricture of the form "S_1 x ... x S_k"

can be expressed in terms of simpler strictures, to wit,

as a conjunction of its k excerpts:

"S_1 x ... x S_k"   =   "S_1_<1>" & ...  & "S_k_<k>".

{| align="center" cellpadding="8" width="90%"

<math>\begin{array}{lll}

& = &

^{\backprime\backprime} \, (S_k)_{[k]} \, ^{\prime\prime}.

\end{array}</math>

In a similar vein, a strait of the form S_1 x ... x S_k

In a similar vein, a strait of the form S_1 x ... x S_k

can be expressed in terms of simpler straits, namely,

can be expressed in terms of simpler straits, namely,