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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="rlvect_1.html#L2" title="RLVECT_1:struct.2">RLSStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">w1</font>, <font color="Maroon" title="c5">w2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">u2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="convfun1.html#K3" title="CONVFUN1:func.3">Prod_of_RLS</a> <font color="Maroon" title="c1">X</font>,<a href="convfun1.html#K4" title="CONVFUN1:func.4">RLS_Real</a> </span>)</span>;<br/>







<b>reconsider </b><font color="Maroon" title="c8">y1</font> = <font color="Maroon" title="c4">w1</font> as   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="convfun1.html#K4" title="CONVFUN1:func.4">RLS_Real</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">y2</font> = <font color="Maroon" title="c5">w2</font> as   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="convfun1.html#K4" title="CONVFUN1:func.4">RLS_Real</a>  ;<br/>
<a NAME="E3:18"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c8">y1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c9">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">w1</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c5">w2</font>
 
<b>by </b><i><a class="ref" href="binop_2.html#D9" title="BINOP_2:def.9">BINOP_2:def 9</a></i>;<br/>
<b>assume </b><a NAME="E4:18"/>
( <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">w1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Maroon" title="c7">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">w2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 ;<br/>

<b>hence </b><a NAME="E5:18"/>
<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c7">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c3">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">w1</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c5">w2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="convfun1.html#E3:18"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="convfun1.html#T2" target="_self" title="CONVFUN1:th.2">Th2</a></i>;<br/>


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