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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">z</font>, <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">t</font>, <font color="Olive" title="b4">y</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">z</font>,<font color="Olive" title="b2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">t</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">z</font> holds <br/> ex <font color="Olive" title="b5">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b4">y</font>,<font color="Olive" title="b2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b4">y</font>,<font color="Olive" title="b1">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">t</font>,<font color="Olive" title="b5">u</font> )</span><br/><b>let </b><font color="Maroon" title="c2">z</font>, <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c5">y</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">z</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">z</font> implies  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> ) )</span><br/>









<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/>

<div><i><font color="Green" title="E25">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><b>then consider </b><font color="Maroon" title="c6">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:34_1"/><i><font color="Green" title="E26">A3</font></i>: 
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c6">u</font> )
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E4:34_1"/>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c6">u</font> )
 <b>by </b><i><a class="txt" href="#E3:34_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E5:34_1"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 ; <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="34_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c3">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><b>consider </b><font color="Maroon" title="c6">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:34_2"/><i><font color="Green" title="E27">A5</font></i>: 
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">p</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T17" target="_self" title="DIRAF:th.17">Th17</a></i>;<br/><a NAME="E4:34_2"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">p</font>
 <b>by </b><i><a class="txt" href="#E3:34_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="diraf.html#D3" target="_self" title="DIRAF:def.3">Def3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E6:34_2"/><i><font color="Green" title="E29">A7</font></i>: 
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> )
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E7:34_2"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="#E1:34_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="#E4:34_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E8:34_2"/><b>then </b>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E10:34_2"/><i><font color="Green" title="E30">A8</font></i>: 
( <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c8">r</font> &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c8">r</font> )
 <b>by </b><i><a class="txt" href="#E3:34_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><div><i><font color="Green" title="E31">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_1"/>
<font color="Maroon" title="c7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E2:34_2_1"/><b>then </b>
( <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="txt" href="#E4:34_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="#E6:34_2"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/><a NAME="E3:34_2_1"/><b>then </b>
<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="#E3:34_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E4:34_2_1"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c4">t</font> )
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="#E1:34_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E5:34_2_1"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c4">t</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E6:34_2_1"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 ; <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><i><font color="Green" title="E32">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_2"/>
<font color="Maroon" title="c7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E2:34_2_2"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">z</font> )
 <b>by </b><i><a class="txt" href="#E4:34_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="#E6:34_2"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/><a NAME="E3:34_2_2"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">z</font> &amp; <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font> )
 <b>by </b><i><a class="txt" href="#E1:34_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="#E3:34_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a>, <a class="ref" href="diraf.html#T6" target="_self" title="DIRAF:th.6">Th6</a></i>;<br/><a NAME="E4:34_2_2"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="diraf.html#T6" target="_self" title="DIRAF:th.6">Th6</a>, <a class="ref" href="diraf.html#T7" target="_self" title="DIRAF:th.7">Th7</a></i>;<br/><a NAME="E5:34_2_2"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E6:34_2_2"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 ; <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="34_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_3"/><i><font color="Green" title="E33">A11</font></i>: 
( <font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E2:34_2_3"/>
( <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="txt" href="#E6:34_2"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="#E10:34_2"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/><a NAME="E3:34_2_3"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c4">t</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="txt" href="#E6:34_2"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="#E1:34_2_3"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="diraf.html#T6" target="_self" title="DIRAF:th.6">Th6</a></i>;<br/><a NAME="E4:34_2_3"/><b>then </b>
( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c8">r</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c8">r</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E5:34_2_3"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 ; <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="E14:34_2"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 <b>by </b><i><a class="txt" href="#E11:34_2"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="#E12:34_2"><i><font color="Green" title="E32">A10</font></i></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="E4:34"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">t</font>,<font color="Olive" title="b1">u</font> )
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="#E2:34"><i><font color="Green" title="E25">A2</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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