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<span class="kw">let </span><font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c2">r2</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">r2</font></span>)</span></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r1</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c2">r2</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">r1</font> = <font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c4">r2</font> = <font color="Maroon" title="c2">r2</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">rr1</font> = <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c3">r1</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span>, <font color="Maroon" title="c6">rr2</font> = <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c4">r2</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 1 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T25" title="EUCLID:th.25">EUCLID:25</a></span>;<br/>
<a NAME="E3:31"/>
<span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">r2</font></span>)</span></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">rr1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c6">rr2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T29" title="RVSUM_1:th.29">RVSUM_1:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:31"/>
<span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">r2</font></span>)</span></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r1</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c2">r2</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T68" title="EUCLID:th.68">EUCLID:68</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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