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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> 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="b3">z</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">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="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">t</font>,<font color="Olive" title="b5">u</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> 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="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E23">A2</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="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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E24">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_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="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c2">x</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span></a><div class="add"><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">p</font>
 <span class="kw">and </span><br/><a NAME="E3:27_1"/><span class="lab"><font color="Green" title="E26">A5</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="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T13" target="_self" onmouseover="rs('diraf/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E4:27_1"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E25">A4</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E6:27_1"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c7">q</font>
 <span class="kw">and </span><br/><a NAME="E7:27_1"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E23">A2</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">assume </span><a NAME="E8:27_1"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c2">x</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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E9:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><a NAME="E10:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E12:27_1"/><span class="lab"><font color="Green" title="E31">A10</font></span>: 
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c8">r</font>
 <span class="kw">and </span><br/><a NAME="E13:27_1"/><span class="lab"><font color="Green" title="E32">A11</font></span>: 
<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="c5">t</font>,<font color="Maroon" title="c8">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><div><span class="lab"><font color="Green" title="E33">A12</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_1_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="c7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:27_1_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" 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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E2:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A13</font></span>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E3:27_1_1"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E4:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E2:27_1_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><a NAME="E5:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><a NAME="E6:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A14</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font>
 ;<br/><a NAME="E7:27_1_1"/>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c5">t</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/><a NAME="E8:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c5">t</font>
 ;<br/><span class="kw">hence </span><a NAME="E9:27_1_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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1_1"><span class="lab"><font color="Green" title="E35">A14</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E34">A15</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_1_2"><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="c7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span></a><div class="add"><a NAME="E1:27_1_2"/><span class="lab"><font color="Green" title="E35">A16</font></span>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><span class="kw">assume </span><a NAME="E2:27_1_2"/><span class="lab"><font color="Green" title="E36">A17</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E3:27_1_2"/>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E4:27_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E2:27_1_2"><span class="lab"><font color="Green" title="E36">A17</font></span></a>, <a class="ref" href="diraf.html#T3" target="_self" onmouseover="rs('diraf/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E5:27_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E1:27_1_2"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="ref" href="diraf.html#T3" target="_self" onmouseover="rs('diraf/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E6:27_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A18</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c2">x</font>
 ;<br/><a NAME="E7:27_1_2"/>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T4" target="_self" onmouseover="rs('diraf/T4')" onmouseout="rh()">Th4</a></span>;<br/><a NAME="E8:27_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>
 ;<br/><span class="kw">hence </span><a NAME="E9:27_1_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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1_2"><span class="lab"><font color="Green" title="E37">A18</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/></div><span class="kw">end;</span></div><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_1_3"><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="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="c2">x</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27_1_3"/><span class="lab"><font color="Green" title="E35">A19</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:27_1_3"/><span class="lab"><font color="Green" title="E36">A20</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><a NAME="E3:27_1_3"/>
<font color="Maroon" title="c2">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="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:27_1"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E4:27_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="#E2:27_1_3"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="ref" href="diraf.html#T3" target="_self" onmouseover="rs('diraf/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E5:27_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A21</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c8">r</font>
 ;<br/><a NAME="E6:27_1_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="c8">r</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E32">A11</font></span></a>, <a class="ref" href="diraf.html#T2" target="_self" onmouseover="rs('diraf/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E7:27_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E1:27_1_3"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="diraf.html#T3" target="_self" onmouseover="rs('diraf/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E8:27_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c8">r</font>
 ;<br/><span class="kw">hence </span><a NAME="E9:27_1_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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1_3"><span class="lab"><font color="Green" title="E37">A21</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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E17:27_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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="txt" href="#E15:27_1"><span class="lab"><font color="Green" title="E34">A15</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/></div><span class="kw">end;</span></div>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_2"><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="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> ) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:27_2"/>
<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c5">t</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">  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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:27_2"/><span class="lab"><font color="Green" title="E25">A22</font></span>: 
( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c6">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="analoaf.html#D5" onmouseover="rs('analoaf/D5')" onmouseout="rh()">ANALOAF:def 5</a></span>;<br/><a NAME="E4:27_2"/>
( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c6">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c6">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_2"><span class="lab"><font color="Green" title="E25">A22</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:27_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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</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>
<span class="kw">hence </span><a NAME="E5:27"/>
 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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E24">A3</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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