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<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</a>;<br/><b>let </b><font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>





<b>thus </b><a NAME="E1:33"/>
( <font color="Maroon" title="c2">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">p</font> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  implies <font color="Maroon" title="c2">r</font> <a href="midsp_1.html#R2" title="MIDSP_1:pred.2">##</a> <font color="Maroon" title="c3">p</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1"/>
<font color="Maroon" title="c2">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">p</font> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a> 
 ;<br/>

<a NAME="E2:33_1"/><b>then </b>
 ex <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Maroon" title="c2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> &amp; <font color="Olive" title="b1">q</font> <a href="midsp_1.html#R2" title="MIDSP_1:pred.2">##</a> <font color="Maroon" title="c3">p</font> )
 
;<br/>
<b>hence </b><a NAME="E3:33_1"/>
<font color="Maroon" title="c2">r</font> <a href="midsp_1.html#R2" title="MIDSP_1:pred.2">##</a> <font color="Maroon" title="c3">p</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:33"/>
( <font color="Maroon" title="c2">r</font> <a href="midsp_1.html#R2" title="MIDSP_1:pred.2">##</a> <font color="Maroon" title="c3">p</font> implies <font color="Maroon" title="c2">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">p</font> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  )
 ;<br/>


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