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<div class="add">

<b>thus </b><a NAME="E1:17"/>
for <font color="Olive" title="b1">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  holds  <a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">z</font>,<font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D7" title="BINOP_1:def.7">BINOP_1:def 7</a>,<a class="ref" href="binop_1.html#D16" title="BINOP_1:def.16">BINOP_1:def 16</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a> ;<br/>

<b>thus </b><a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font> = 
0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">w</font>
<b>by </b><i><a class="ref" href="binop_2.html#D15" target="_self" title="BINOP_2:def.15">Def15</a></i>
<br/>.= 
<font color="Maroon" title="c3">w</font>

;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D17" title="BINOP_1:def.17">BINOP_1:def 17</a><br/>

<b>thus </b><a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">z</font> = 
<font color="Maroon" title="c3">w</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0
<b>by </b><i><a class="ref" href="binop_2.html#D15" target="_self" title="BINOP_2:def.15">Def15</a></i>
<br/>.= 
<font color="Maroon" title="c3">w</font>

;<br/>


</div>
