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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  holds <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  implies ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:31"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:31"/>
( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="diraf.html#E37"><span class="lab"><font color="Green" title="E22">Lm3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E3:31"/>
( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="diraf.html#E37"><span class="lab"><font color="Green" title="E22">Lm3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a> </span><br/>

<span class="kw">hence </span><a NAME="E4:31"/>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="diraf.html#E37"><span class="lab"><font color="Green" title="E22">Lm3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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