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<span class="kw">reconsider </span><font color="Maroon" title="c1">N</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  as   <a href="supinf_2.html#NM1" title="SUPINF_2:NM.1">Denum_Set_of_R_EAL</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#D8" target="_self" title="SUPINF_2:def.8">Def14</a>, <a class="ref" href="supinf_2.html#T34" target="_self" title="SUPINF_2:th.34">Th52</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c1">N</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">N</font> is  <a href="supinf_2.html#V5" title="SUPINF_2:attr.5">nonnegative</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:46_1_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="supinf_1.html#NM1" title="SUPINF_1:NM.1">R_eal</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">N</font> holds <br/> <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="supinf_2.html#D9" target="_self" title="SUPINF_2:def.9">SUPINF_2:def 9</a> <a class="txt" 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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