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<b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of  <a href="midsp_1.html#K13" title="MIDSP_1:func.13">setvect</a> <font color="Maroon" title="c1">M</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:69_1_2"/><i><font color="Green" title="E48">A3</font></i>: 
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K13" title="MIDSP_1:func.13">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font>
 <b>and </b><br/><a NAME="E2:69_1_2"/><i><font color="Green" title="E49">A4</font></i>: 
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K13" title="MIDSP_1:func.13">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font>
 ;<br/>

<a NAME="E3:69_1_2"/>
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K13" title="MIDSP_1:func.13">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">W</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K13" title="MIDSP_1:func.13">setvect</a> <font color="Maroon" title="c1">M</font>;<br/>

<a NAME="E1:69_1_2_1"/><i><font color="Green" title="E50">A5</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="txt" href="midsp_1.html#E1:69_1_2"><i><font color="Green" title="E48">A3</font></i></a></i>;<br/>
<a NAME="E2:69_1_2_1"/>
<font color="Maroon" title="c4">W</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="txt" href="midsp_1.html#E2:69_1_2"><i><font color="Green" title="E49">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:69_1_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">W</font>
 <b>by </b><i><a class="txt" href="midsp_1.html#E1:69_1_2_1"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="midsp_1.html#T78" target="_self" title="MIDSP_1:th.78">Th78</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:69_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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