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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">KX</font> being    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">SX</font> being    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Olive" title="b1">KX</font><br/>  for <font color="Olive" title="b3">S1</font> being    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Olive" title="b2">SX</font>  st <font color="Olive" title="b2">SX</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  &amp; <font color="Olive" title="b3">S1</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  holds <br/><font color="Olive" title="b3">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Olive" title="b1">KX</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">KX</font> be    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</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">SX</font> being    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font><br/>  for <font color="Olive" title="b2">S1</font> being    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Olive" title="b1">SX</font>  st <font color="Olive" title="b1">SX</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  &amp; <font color="Olive" title="b2">S1</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  holds <br/><font color="Olive" title="b2">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">SX</font> be    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</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">S1</font> being    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c3">SX</font>  st <font color="Maroon" title="c3">SX</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  &amp; <font color="Olive" title="b1">S1</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  holds <br/><font color="Olive" title="b1">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">S1</font> be    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c3">SX</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"> ( <font color="Maroon" title="c3">SX</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  &amp; <font color="Maroon" title="c4">S1</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>  implies <font color="Maroon" title="c4">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font> )</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">s1</font> = <font color="Maroon" title="c4">S1</font> as    <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#T27" target="_self" onmouseover="rs('simplex0/T27')" onmouseout="rh()">Th27</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:89"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c3">SX</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a> 
 <span class="kw">and </span><br/><a NAME="E3:89"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c4">S1</font> is  <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</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">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font></span><br/>

<a NAME="E4:89"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">SX</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D13" target="_self" onmouseover="rs('simplex0/D13')" onmouseout="rh()">Def13</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="89_1"><span class="kw">now </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">  for <font color="Olive" title="b1">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">s1</font>  st <font color="Olive" title="b1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">KX</font> holds <br/><font color="Olive" title="b1">A</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">s1</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"> ( <font color="Maroon" title="c6">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">KX</font> implies <font color="Maroon" title="c6">A</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">A</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">SX</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:89"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:89_1"/>
<font color="Maroon" title="c6">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">KX</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"> <font color="Maroon" title="c6">A</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a> </span><br/><a NAME="E3:89_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:89"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>;<br/><a NAME="E4:89_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">SX</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:89_1"/>
<font color="Maroon" title="c6">A</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:89"><span class="lab"><font color="Green" title="E38">A2</font></span></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:89"/>
<font color="Maroon" title="c4">S1</font> is   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D14" target="_self" onmouseover="rs('simplex0/D14')" onmouseout="rh()">Def14</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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