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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font>, <font color="Olive" title="b5">u</font>, <font color="Olive" title="b6">w</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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">w</font> holds <br/><font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">w</font></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font>, <font color="Maroon" title="c5">t</font>, <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c7">w</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> implies <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> )</span><br/>













<b>assume </b><b>that </b><br/><a NAME="E1:27"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green" title="E18">A2</font></i>: 
( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font></span><br/>

<a NAME="E3:27"/><i><font color="Green" title="E19">A3</font></i>: 
( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> or <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c6">u</font> )
 
<b>by </b><i><a class="txt" href="diraf.html#E2:27"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/>
<div><i><font color="Green" title="E20">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_1"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font></span><br/><a NAME="E2:27_1"/><b>then </b>
( <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> or <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c6">u</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:27"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="diraf.html#E3:27"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><b>hence </b><a NAME="E3:27_1"/>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font>
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_2"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font></span><br/><a NAME="E2:27_2"/><b>then </b>
( <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> or <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c6">u</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:27"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="diraf.html#E3:27"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E3:27_2"/><b>then </b>
( <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c6">u</font> or <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font> )
 <b>by </b><i><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><b>hence </b><a NAME="E4:27_2"/>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font>
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:27"/>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">w</font>
 <b>by </b><i><a class="txt" href="diraf.html#E2:27"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="diraf.html#E4:27"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</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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