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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"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> holds <br/><font color="Olive" title="b1">A</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> implies <font color="Maroon" title="c2">A</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font> )</span><br/>



<b>assume </b><a NAME="E1:52"/>
<font color="Maroon" title="c2">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font></span><br/>

<b>then consider </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E3:52"/><i><font color="Green" title="E47">A1</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#D3" target="_self" title="AFF_1:def.3">Def3</a></i>;<br/>
<a NAME="E4:52"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" target="_self" title="AFF_1:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E5:52"/>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="#E3:52"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="aff_1.html#T51" target="_self" title="AFF_1:th.51">Th51</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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