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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="valuat_1.html#M1" target="_self">interpretation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:37_1"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="valuat_1.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E2:37_1"/><b>then </b><i><font color="Green">E25</font></i>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  implies <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><a NAME="E3:37_1"/>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  implies <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  )
 <b>by </b><i><a class="txt" href="valuat_1.html#E1:37_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="margrel1.html#T51">MARGREL1:51</a></i>;<br/><b>hence </b><a NAME="E4:37_1"/>
<span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="valuat_1.html#E2:37_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:37"/>
 <a href="valuat_1.html#K12" target="_self">Valid</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a>  <a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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