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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> implies <font color="Maroon" title="c1">AS</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> )</span><br/>

<b>assume </b><a NAME="E1:68"/>
<font color="Maroon" title="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">AS</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a></span><br/>

<a NAME="E2:68"/><b>then </b>
for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">C</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><br/> for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">a'</font>, <font color="Olive" title="b8">b'</font>, <font color="Olive" title="b9">c'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b1">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b7">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b8">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b9">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b1">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b2">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b3">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">a'</font>,<font color="Olive" title="b8">b'</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">a'</font>,<font color="Olive" title="b9">c'</font> holds <br/><font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">b'</font>,<font color="Olive" title="b9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_4.html#T51" target="_self" title="AFF_4:th.51">Th51</a></i>;<br/>
<b>hence </b><a NAME="E3:68"/>
<font color="Maroon" title="c1">AS</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a>
 <b>by </b><i><a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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