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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L2">RLSStruct</a> , <font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L2">RLSStruct</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="convfun1.html#K3" target="_self">Prod_of_RLS</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="real_1.html#NM1">Real</a>;<br/>









<a NAME="E1:5"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="convfun1.html#K2" target="_self">Mult_in_Prod_of_RLS</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">p</font>,<font color="Maroon">u</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D4">RLVECT_1:def 4</a></i>;<br/>
<a NAME="E2:5"/><i><font color="Green">E38</font></i>: 
( the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">X</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">p</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font> &amp; the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">Y</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">p</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D4">RLVECT_1:def 4</a></i>;<br/>
<b>assume </b><a NAME="E3:5"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span>
 ;<br/>

<b>hence </b><a NAME="E4:5"/>
<font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i>, , </i>;<br/>


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