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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <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">  for <font color="Olive" title="b1">Af</font> being   <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds   <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Olive" title="b1">Af</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Af</font> be   <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</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">  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c2">Af</font></span><br/>



<a NAME="E1:20"/>
<font color="Maroon" title="c2">Af</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c2">Af</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topdim_1.html#D5" target="_self" onmouseover="rs('topdim_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E2:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<span class="p1">(<span class="default"><a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c2">Af</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <font color="Maroon" title="c1">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/>
<a NAME="E3:20"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
;<br/>
<span class="kw">hence </span><a NAME="E4:20"/>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c2">Af</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>; <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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