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<b>let </b><font color="Maroon">g1</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<span class="p2">(<span class="default"><a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font>, <font color="Maroon">g2</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<span class="p2">(<span class="default"><a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E1:76_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a><br/> for <font color="Olive">e</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font> holds  <font color="Maroon">g1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">e</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="rlvect_2.html#K8" target="_self">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K12" target="_self">@</a> <font color="Olive">e</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:76_1_2"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a><br/> for <font color="Olive">e</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font> holds  <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">e</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="rlvect_2.html#K8" target="_self">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K12" target="_self">@</a> <font color="Olive">e</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">e</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="rlvect_2.html#K11" target="_self">LinComb</a> <font color="Maroon">V</font>;<br/><b>thus </b><font color="Maroon">g1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">e</font> = 
<font color="Maroon">x</font> <a href="rlvect_2.html#K8" target="_self">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K12" target="_self">@</a> <font color="Maroon">e</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">g2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="rlvect_2.html#T4" target="_self">Th4</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:76_1_2"/>
<font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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