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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">A</font>, <font color="Olive" title="b2">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b1">A</font></span>)</span>  st <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b2">B</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  holds <br/>( <font color="Olive" title="b3">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Olive" title="b2">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <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">  for <font color="Olive" title="b1">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c3">B</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  holds <br/>( <font color="Olive" title="b1">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c3">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</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"> ( <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c3">B</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  implies ( <font color="Maroon" title="c4">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c3">B</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c3">B</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</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"> ( <font color="Maroon" title="c4">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<a NAME="E3:45"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="metrizts.html#T9" onmouseover="rs('metrizts/T9')" onmouseout="rh()">METRIZTS:9</a></span>;<br/>
<a NAME="E4:45"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="topdim_1.html#T18" target="_self" onmouseover="rs('topdim_1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<span class="kw">then </span> <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c4">F</font> = 
 <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="topdim_1.html#E28"><span class="lab"><font color="Green" title="E20">Lm5</font></span></a></span>
<br/>.= 
 <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="metrizts.html#T9" onmouseover="rs('metrizts/T9')" onmouseout="rh()">METRIZTS:9</a></span>
<br/>.= 
 <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c3">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="topdim_1.html#E28"><span class="lab"><font color="Green" title="E20">Lm5</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:45"/>
( <font color="Maroon" title="c4">F</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Maroon" title="c3">B</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="topdim_1.html#T18" target="_self" onmouseover="rs('topdim_1/T18')" onmouseout="rh()">Th18</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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