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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> ;<br/><b>let </b><font color="Maroon">x1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">X</font>, <font color="Maroon">x2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">w1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">w2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">u1</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>,<a href="convfun1.html#K4" target="_self">RLS_Real</a> </span>)</span>, <font color="Maroon">u2</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>,<a href="convfun1.html#K4" target="_self">RLS_Real</a> </span>)</span>;<br/>







<b>reconsider </b><font color="Maroon">y1</font> = <font color="Maroon">w1</font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <a href="convfun1.html#K4" target="_self">RLS_Real</a>  ;<br/>
<b>reconsider </b><font color="Maroon">y2</font> = <font color="Maroon">w2</font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <a href="convfun1.html#K4" target="_self">RLS_Real</a>  ;<br/>
<i><font color="Green">E34</font></i>: <font color="Maroon">y1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">y2</font> = 
the <a href="rlvect_1.html#U1">add</a> of <a href="convfun1.html#K4" target="_self">RLS_Real</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">w1</font>,<font color="Maroon">w2</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">w1</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">w2</font>
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
;<br/>
<b>assume </b><a NAME="E4:18"/>
( <font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">w1</font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">u2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">w2</font></span><a href="domain_1.html#K1">]</a></span> )
 ;<br/>

<b>hence </b><a NAME="E5:18"/>
<font color="Maroon">u1</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">u2</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">x1</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">w1</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">w2</font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i>, </i>;<br/>


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