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<b>let </b><font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c2">r2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c3">fr1</font>, <font color="Maroon" title="c4">fr2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">F_Real</a> ;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green" title="E1">A1</font></i>: 
( <font color="Maroon" title="c1">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fr1</font> &amp; <font color="Maroon" title="c2">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">fr2</font> )
 ;<br/>

<a NAME="E2:1"/>
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">F_Real</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">fr1</font>,<font color="Maroon" title="c4">fr2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:1"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:1"/>
<font color="Maroon" title="c1">r1</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c2">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fr1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c4">fr2</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/>


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