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<a NAME="E1:17_1_1"/>
 <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T17" title="TOPMETR:th.17">TOPMETR:17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">P</font> =  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">P</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">P</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c2">P</font> is  <a href="xxreal_2.html#V6" title="XXREAL_2:attr.6">interval</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:17_1_1"/>
 not <font color="Maroon" title="c2">P</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <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="c2">P</font> is  <a href="xxreal_2.html#V6" title="XXREAL_2:attr.6">interval</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xxreal_2.html#D12" title="XXREAL_2:def.12">XXREAL_2:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> or  not <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> or <a href="xxreal_1.html#K1" title="XXREAL_1:func.1">K58</a>(<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:17_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="xxreal_1.html#K1" title="XXREAL_1:func.1">K58</a>(<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c4">b</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E6:17_1_1"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E7:17_1_1"/>
<a href="xxreal_1.html#K1" title="XXREAL_1:func.1">K58</a>(<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 ; <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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