Changes

The column for E''J'' is computed by means of the following chain of identities, where the contingent variables ''u''′ and ''v''′ are defined as ''u''′ = ''u'' + d''u'' and ''v''′ = ''v'' + d''v''.

The column for E''J'' is computed by means of the following chain of identities, where the contingent variables ''u''′ and ''v''′ are defined as ''u''′ = ''u'' + d''u'' and ''v''′ = ''v'' + d''v''.

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o--------------------------------------------------------------o

{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"

|                                                             |

|

|   EJ<u, v, du, dv>  =   J<u + du, v + dv>  =   J<u', v'>  |

{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"

|                                                             |

| E''J''‹''u'', ''v'', d''u'', d''v''›

| =

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| ''J''‹''u'' + d''u'', ''v'' + d''v''›

| =

| ''J''‹''u''’, ''v''’›

|}

|}

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This makes it easy to determine E''J'' by inspection, computing the conjunction ''J''‹''u''&prime;,&nbsp;''v''&prime;›&nbsp;=&nbsp;''u''&prime;&nbsp;''v''&prime; from the columns headed ''u''&prime; and ''v''&prime;.  Since all of these forms express the same proposition E''J'' in E''U''^&nbsp;&bull;, the dependence on d''u'' and d''v'' is still present but merely left implicit in the final variant ''J''‹''u''&prime;,&nbsp;''v''&prime;›.

This makes it easy to determine E''J'' by inspection, computing the conjunction ''J''‹''u''&prime;,&nbsp;''v''&prime;›&nbsp;=&nbsp;''u''&prime;&nbsp;''v''&prime; from the columns headed ''u''&prime; and ''v''&prime;.  Since all of these forms express the same proposition E''J'' in E''U''^&nbsp;&bull;, the dependence on d''u'' and d''v'' is still present but merely left implicit in the final variant ''J''‹''u''&prime;,&nbsp;''v''&prime;›.