Changes

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<li>

<p>In a setting where the connection <math>F\!</math> is fixed but the imagination <math>\underline{f}</math> is allowed to vary over a wide range of possibilities, call <math>p\!</math> the ''stretch of <math>F\!</math> to <math>\underline{f}</math> on <math>X,\!</math>'' and write it in the style <math>F^\$ \underline{f},</math> exactly as if "F$" denotes an operator F$ : (X -> B)^k -> (X -> B) that is derived from F and applied to f, ultimately yielding a proposition F$f : X -> B.</p></li>

<p>In a setting where the connection <math>F\!</math> is fixed but the imagination <math>\underline{f}</math> is allowed to vary over a wide range of possibilities, call <math>p\!</math> the ''stretch of <math>F\!</math> to <math>\underline{f}</math> on <math>X,\!</math>'' and write it in the style <math>F^\$ \underline{f},</math> exactly as if <math>^{\backprime\backprime} F^\$ \, ^{\prime\prime}</math> denotes an operator F$ : (X -> B)^k -> (X -> B) that is derived from F and applied to f, ultimately yielding a proposition F$f : X -> B.</p></li>

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<li>

<p>In a setting where the imagination<math>\underline{f}</math> is fixed but the connection <math>F\!</math> is allowed to range over wide variety of possibilities, call <math>p\!</math> the ''stretch of <math>\underline{f}</math> by <math>F\!</math> to <math>\underline\mathbb{B},</math>'' and write it in the style "f$F", exactly as if "f$" denotes an operator f$ : (B^k -> B) -> (X -> B) that is derived from f and applied to F, ultimately yielding a proposition f$F : X -> B.</p></li>

<p>In a setting where the imagination<math>\underline{f}</math> is fixed but the connection <math>F\!</math> is allowed to range over wide variety of possibilities, call <math>p\!</math> the ''stretch of <math>\underline{f}</math> by <math>F\!</math> to <math>\underline\mathbb{B},</math>'' and write it in the style <math>\underline{f}^\$ F,</math> exactly as if <math>^{\backprime\backprime} \underline{f}^\$ \, ^{\prime\prime}</math> denotes an operator f$ : (B^k -> B) -> (X -> B) that is derived from f and applied to F, ultimately yielding a proposition f$F : X -> B.</p></li>

</ol>

</ol>