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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</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">X1</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c1">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c4">Z</font> implies <font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c4">Z</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c1">X1</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">X2</font>
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c1">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c4">Z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c4">Z</font></span><br/>

<a NAME="E3:28"/>
<font color="Maroon" title="c1">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E1:28"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="cqc_the3.html#T25" target="_self" title="CQC_THE3:th.25">Th25</a></i>;<br/>
<a NAME="E4:28"/><b>then </b>
 <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T20" target="_self" title="CQC_THE3:th.20">Th20</a></i>;<br/>
<a NAME="E5:28"/><b>then </b>
<font color="Maroon" title="c4">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E2:28"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E6:28"/>
<font color="Maroon" title="c2">X2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c4">Z</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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