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<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 P the "stretch of F to f on U", and write it in the style "F$f", exactly as if "F$" denotes an operator F$ : (U -> B)k -> (U -> B) that is derived from F and applied to f, ultimately yielding a proposition F$f : U -> 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 P the "stretch of F to f on X", and write it in the style "F$f", exactly as if "F$" 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>

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<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 P the "stretch of f by F to B", and write it in the style "f$F", exactly as if "f$" denotes an operator f$ : (Bk -> B) -> (U -> B) that is derived from f and applied to F, ultimately yielding a proposition f$F : U -> 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 P the "stretch of f by F to B", 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>

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