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<span class="kw">let </span><font color="Maroon" title="c2">T</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</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">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  implies <font color="Maroon" title="c2">T</font> is  <a href="topalg_2.html#V2" title="TOPALG_2:attr.2">interval</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:20"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</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">T</font> is  <a href="topalg_2.html#V2" title="TOPALG_2:attr.2">interval</a> </span><br/>

<a NAME="E2:20"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <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="c3">P</font> =  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>
<a NAME="E4:20"/>
<font color="Maroon" title="c3">P</font> is  <a href="xxreal_2.html#V6" title="XXREAL_2:attr.6">interval</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:20"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font> is  <a href="xxreal_2.html#V6" title="XXREAL_2:attr.6">interval</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="topalg_2.html#D3" target="_self" title="TOPALG_2:def.3">TOPALG_2:def 3</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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