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<b>let </b><font color="Maroon" title="c1">X</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> ;<br/>

<div><i><font color="Green" title="E17">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="cqc_the3.html#R3" title="CQC_THE3:pred.3">|-</a> <font color="Maroon" title="c1">X</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</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> ;<br/><b>assume </b><a NAME="E1:16_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E2:16_1_1"/><b>then </b>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:16_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="cqc_the3.html#D3" target="_self" title="CQC_THE3:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E3:16_1_1"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:16_1"/>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D2" target="_self" title="CQC_THE3:def.2">Def2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green" title="E18">A3</font></i>: 
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</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> ;<br/><b>assume </b><a NAME="E1:16_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E2:16_2_1"/><b>then </b>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:16_2"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="cqc_the3.html#D2" target="_self" title="CQC_THE3:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:16_2_1"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:16_2"/>
 <a href="cqc_the3.html#R3" title="CQC_THE3:pred.3">|-</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D3" target="_self" title="CQC_THE3:def.3">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
(  <a href="cqc_the3.html#R3" title="CQC_THE3:pred.3">|-</a> <font color="Maroon" title="c1">X</font> iff  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:16"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


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