<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">t</font>, <font color="Maroon" title="c4">u</font> be   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</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="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; (  for <font color="Olive" title="b1">t</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c3">t</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b1">t</font> ) &amp; <font color="Maroon" title="c4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; (  for <font color="Olive" title="b1">t</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c4">u</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b1">t</font> ) implies <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:69_1_2"/><span class="lab"><font color="Green" title="E45">A7</font></span>: 
( <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; (  for <font color="Olive" title="b1">s</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c3">t</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b1">s</font> ) &amp; <font color="Maroon" title="c4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; (  for <font color="Olive" title="b1">s</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c4">u</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b1">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="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font></span><br/>

<a NAME="E2:69_1_2"/>
( <font color="Maroon" title="c3">t</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Maroon" title="c4">u</font> &amp; <font color="Maroon" title="c4">u</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Maroon" title="c3">t</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_2"><span class="lab"><font color="Green" title="E45">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:69_1_2"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T23" target="_self" onmouseover="rs('qc_lang1/T23')" onmouseout="rh()">Th23</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>
