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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="midsp_1.html#NM1">MidSp</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:62"/>
( <font color="Maroon">c<sub>2</sub></font> is    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="midsp_1.html#K14" target="_self">setvect</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>thus </b><a NAME="E2:62"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="midsp_1.html#K14" target="_self">setvect</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> is    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">c<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:62_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="midsp_1.html#K14" target="_self">setvect</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:62_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">c<sub>1</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:62_1"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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


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