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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#NM2" title="BINOP_1:NM.2">BinOp</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="E1:66_1_2"/><i><font color="Green" title="E48">A3</font></i>: 
for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</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="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u1</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <font color="Olive" title="b2">v1</font>
 <b>and </b><br/><a NAME="E2:66_1_2"/><i><font color="Green" title="E49">A4</font></i>: 
for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</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="c3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u1</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <font color="Olive" title="b2">v1</font>
 ;<br/>

<a NAME="E3:66_1_2"/>
for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</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="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c5">v1</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="E1:66_1_2_1"/><i><font color="Green" title="E50">A5</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u1</font> <a href="midsp_1.html#K14" title="MIDSP_1:func.14">+</a> <font color="Maroon" title="c5">v1</font>
 
<b>by </b><i><a class="txt" href="midsp_1.html#E1:66_1_2"><i><font color="Green" title="E48">A3</font></i></a></i>;<br/>
<a NAME="E2:66_1_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font>
 
<b>by </b><i><a class="txt" href="midsp_1.html#E2:66_1_2"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="midsp_1.html#E1:66_1_2_1"><i><font color="Green" title="E50">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:66_1_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:66_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="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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