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<span class="kw">reconsider </span><font color="Maroon" title="c4">n</font> = <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">R1</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">R2</font> = <font color="Maroon" title="c3">y</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>
<a NAME="E3:9_1_1"/>
<font color="Maroon" title="c5">R1</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <font color="Maroon" title="c6">R2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:9_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="valued_1.html#K1" title="VALUED_1:func.1">+</a> <font color="Maroon" title="c3">y</font> is    <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> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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