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<b>let </b><font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">fr1</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a> , <font color="Maroon">fr2</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a> ;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fr1</font> &amp; <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fr2</font> )
 ;<br/>

<a NAME="E2:1"/>
the <a href="rlvect_1.html#U1">add</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">fr1</font>,<font color="Maroon">fr2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">r1</font>,<font color="Maroon">r2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:1"/>
<font color="Maroon">r1</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fr1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">fr2</font>
 <b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>;<br/>


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