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The computational scheme shown in Table&nbsp;36 treated <math>J\!</math> as a proposition in <math>U^\bullet\!</math> and formed <math>\boldsymbol\varepsilon J\!</math> as a proposition in <math>\mathrm{E}U^\bullet.\!</math>  When <math>J\!</math> is regarded as a mapping <math>J : U^\bullet \to X^\bullet\!</math> then <math>\boldsymbol\varepsilon J\!</math> must be obtained as a mapping <math>\boldsymbol\varepsilon J : \mathrm{E}U^\bullet \to X^\bullet.\!</math>  By default, the tacit extension of the map <math>J : [u, v] \to [x]\!</math> is naturally taken to be a particular map, one that has the following form:

The computational scheme shown in Table&nbsp;36 treated <math>J\!</math> as a proposition in <math>U^\bullet\!</math> and formed <math>\boldsymbol\varepsilon J\!</math> as a proposition in <math>\mathrm{E}U^\bullet.\!</math>  When <math>J\!</math> is regarded as a mapping <math>J : U^\bullet \to X^\bullet\!</math> then <math>\boldsymbol\varepsilon J\!</math> must be obtained as a mapping <math>\boldsymbol\varepsilon J : \mathrm{E}U^\bullet \to X^\bullet.\!</math>  By default, the tacit extension of the map <math>J : [u, v] \to [x]\!</math> is naturally taken to be a particular map,

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| <math>\boldsymbol\varepsilon J : [u, v, \mathrm{d}u, \mathrm{d}v] \to [x] \subseteq [x, \mathrm{d}x].\!</math>

| <math>\boldsymbol\varepsilon J : [u, v, \mathrm{d}u, \mathrm{d}v] \to [x] \subseteq [x, \mathrm{d}x],\!</math>

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This is the map that looks like <math>J\!</math> when painted in the frame of the extended source universe and that takes the same thematic variable in the extended target universe as the one that <math>J\!</math> already employs.

namely, the one that looks like <math>J\!</math> when painted in the frame of the extended source universe and that takes the same thematic variable in the extended target universe as the one that <math>J\!</math> already takes.

But the choice of a particular thematic variable, for example <math>x\!</math> for <math>\check{J},\!</math> is a shade more arbitrary than the initial choice of variable names <math>\{ u, v \}.\!</math> This means that the map we are calling the ''trope extension'', namely:

But the choice of a particular thematic variable, for example <math>x\!</math> for <math>\check{J},\!</math> is a shade more arbitrary than the choice of original variable names <math>\{ u, v \},\!</math> so the map we are calling the ''trope extension'',

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since it looks just the same as <math>\boldsymbol\varepsilon J\!</math> in the way that its fibers paint the source domain, belongs just as fully to the family of tacit extensions, generically considered.

since it looks just the same as <math>\boldsymbol\varepsilon J\!</math> in the way its fibers paint the source domain, belongs just as fully to the family of tacit extensions, generically considered.

These considerations have the practical consequence that all of our computations and illustrations of <math>\epsilon</math>''J'' perform the double duty of capturing an image of <math>\eta</math>''J'' as well.  In other words, we are saved the work of carrying out calculations and drawing figures for the trope extension <math>\eta</math>''J'', because the exercise would be identical to the work already done for <math>\epsilon</math>''J''. Since the computations given for <math>\epsilon</math>''J'' are expressed solely in terms of the variables {''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''}, these variables work equally well for finding <math>\eta</math>''J''. Furthermore, since each of the above Figures shows only how the level sets of <math>\epsilon</math>''J'' partition the extended source universe E''U''^&nbsp;&bull;&nbsp;=&nbsp;[''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''], all of them serve equally well as portraits of <math>\eta</math>''J''.

These considerations have the practical consequence that all of our computations and illustrations of <math>\boldsymbol\varepsilon J\!</math> perform the double duty of capturing <math>\eta J\!</math> as well.  In other words, we are saved the work of carrying out calculations and drawing figures for the trope extension <math>\eta J,\!</math> because it would be identical to the work already done for <math>\boldsymbol\varepsilon J.\!</math>  Since the computations given for <math>\boldsymbol\varepsilon J\!</math> are expressed solely in terms of the variables <math>\{ u, v, \mathrm{d}u, \mathrm{d}v \},\!</math> they work equally well for finding <math>\eta J.\!</math>  Further, since each of the above Figures shows only how the level sets of <math>\boldsymbol\varepsilon J\!</math> partition the extended source universe <math>\mathrm{E}U^\bullet = [u, v, \mathrm{d}u, \mathrm{d}v],\!</math> all of them serve equally well as portraits of <math>\eta J.\!</math>

=====Enlargement Map of Conjunction=====

=====Enlargement Map of Conjunction=====