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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:38"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:38"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c3">r</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></span>;<br/>
<a NAME="E4:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#D1" target="_self" title="CQC_THE3:def.1">Def1</a></span>;<br/>
<a NAME="E5:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<a NAME="E6:38"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T31" target="_self" title="CQC_THE3:th.31">Th31</a></span>;<br/>
<a NAME="E7:38"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></span>;<br/>
<a NAME="E8:38"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></span>;<br/>
<a NAME="E9:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#D1" target="_self" title="CQC_THE3:def.1">Def1</a></span>;<br/>
<a NAME="E10:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<a NAME="E11:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="cqc_the3.html#E39"><span class="lab"><font color="Green" title="E31">Lm2</font></span></a></span>;<br/>
<a NAME="E12:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T10" target="_self" title="CQC_THE3:th.10">Th10</a></span>;<br/>
<a NAME="E13:38"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:38"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="cqc_the3.html#T9" target="_self" title="CQC_THE3:th.9">Th9</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T11" target="_self" title="CQC_THE3:th.11">Th11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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