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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>, <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/><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>, <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" 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> <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/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:21"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:21"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:21"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<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" 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="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="E4:21"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E17">A3</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E19">A5</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">now </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="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> 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></a><div class="add"><span class="kw">assume </span><a NAME="E1:21_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="c5">t</font>,<font color="Maroon" title="c4">z</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="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="E2:21_1"/><span class="kw">then </span>
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><a NAME="E3:21_1"/><span class="kw">then </span>
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:21_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>
 ; <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/></div><span class="kw">end;</span></div>
<a NAME="E6:21"/>
( <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> 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:21"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E19">A5</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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