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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a>  <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>2</sub></font> = 
the <a href="rlvect_1.html#U1">add</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>

<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="int_3.html#E1:12"><i><font color="Green">E8</font></i></a>, <a class="ref" href="gr_cy_1.html#T14">GR_CY_1:14</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="int_3.html#K1" target="_self">INT.Ring</a> 
<b>by </b><i><a class="txt" href="int_3.html#E5"><i><font color="Green">Lemma3</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:12"/>
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T19">RLVECT_1:19</a></i>;<br/>


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