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

<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c4">s</font> implies <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:38"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font>
 <b>and </b><br/><a NAME="E2:38"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c4">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="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E3:38"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E1:38"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></i>;<br/>
<a NAME="E4:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#D1" target="_self" title="CQC_THE3:def.1">Def1</a></i>;<br/>
<a NAME="E5:38"/><b>then </b><i><font color="Green" title="E36">A3</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T4" target="_self" title="CQC_THE3:th.4">Th4</a>, <a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/>
<a NAME="E6:38"/>
<font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E2:38"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></i>;<br/>
<a NAME="E7:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#D1" target="_self" title="CQC_THE3:def.1">Def1</a></i>;<br/>
<a NAME="E8:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T4" target="_self" title="CQC_THE3:th.4">Th4</a>, <a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/>
<a NAME="E9:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E5:38"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="cqc_the3.html#E39"><i><font color="Green" title="E31">Lm2</font></i></a></i>;<br/>
<a NAME="E10:38"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self" title="CQC_THE3:th.10">Th10</a></i>;<br/>
<a NAME="E11:38"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T31" target="_self" title="CQC_THE3:th.31">Th31</a></i>;<br/>
<a NAME="E12:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></i>;<br/>
<a NAME="E13:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E10:38"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="cqc_the3.html#T9" target="_self" title="CQC_THE3:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E14:38"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T11" target="_self" title="CQC_THE3:th.11">Th11</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>
