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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">C</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> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Olive" title="b2">C</font> holds <br/><font color="Olive" title="b2">C</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">C</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c3">C</font> implies <font color="Maroon" title="c3">C</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:55"/>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c3">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">C</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E3:55"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E4:55"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 <span class="kw">and </span><br/><a NAME="E5:55"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font>
 <span class="kw">and </span><br/><a NAME="E6:55"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
<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="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 <span class="kw">and </span><br/><a NAME="E7:55"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c3">C</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="c6">c</font>,<font color="Maroon" title="c7">d</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T37" target="_self" title="AFF_1:th.37">Th51</a></span>;<br/>
<a NAME="E8:55"/>
<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="aff_1.html#T4" target="_self" title="AFF_1:th.4">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:55"/>
<font color="Maroon" title="c3">C</font> <a href="aff_1.html#R3" title="AFF_1:pred.3">//</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E6:55"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E7:55"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="aff_1.html#T37" target="_self" title="AFF_1:th.37">Th51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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