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<b>let </b><font color="Maroon" title="c1">Y0</font>, <font color="Maroon" title="c2">Y1</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D0</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font><br/> for <font color="Olive" title="b2">D1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>  st  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y0</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font> #) &amp; <font color="Olive" title="b1">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">D1</font> &amp; <font color="Olive" title="b1">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> holds <br/><font color="Olive" title="b2">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a></span><br/><b>let </b><font color="Maroon" title="c3">D0</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>  st  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y0</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font> #) &amp; <font color="Maroon" title="c3">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D1</font> &amp; <font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> holds <br/><font color="Olive" title="b1">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a></span><br/><b>let </b><font color="Maroon" title="c4">D1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y0</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font> #) &amp; <font color="Maroon" title="c3">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D1</font> &amp; <font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> implies <font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> )</span><br/>





<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y0</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D1</font> or  not <font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> or <font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> )</span><br/>

<b>assume </b><a NAME="E2:29"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> or <font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> )</span><br/>

<b>assume </b><a NAME="E3:29"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a></span><br/>

<a NAME="E4:29"/><b>then </b>
<font color="Maroon" title="c3">D0</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 
<b>by </b><i><a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></i>;<br/>
<a NAME="E5:29"/><b>then </b><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 
<b>by </b><i><a class="txt" href="tex_4.html#E1:29"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="tex_4.html#E2:29"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="tex_4.html#T6" target="_self" title="TEX_4:th.6">Th6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">D</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a> &amp; <font color="Maroon" title="c4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font> implies <font color="Maroon" title="c4">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font> )</span><br/><b>assume </b><a NAME="E1:29_1"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c5">D</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font> implies <font color="Maroon" title="c4">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font> )</span><br/><b>assume </b><a NAME="E2:29_1"/><i><font color="Green" title="E23">A6</font></i>: 
<font color="Maroon" title="c4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font></span><br/><b>reconsider </b><font color="Maroon" title="c6">E</font> = <font color="Maroon" title="c5">D</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font> <b>by </b><i><a class="txt" href="tex_4.html#E1:29"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/><a NAME="E4:29_1"/>
( <font color="Maroon" title="c6">E</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a> &amp; <font color="Maroon" title="c3">D0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">E</font> )
 <b>by </b><i><a class="txt" href="tex_4.html#E1:29"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="tex_4.html#E2:29"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="tex_4.html#E1:29_1"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="tex_4.html#E2:29_1"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="tex_4.html#T6" target="_self" title="TEX_4:th.6">Th6</a></i>;<br/><b>hence </b><a NAME="E5:29_1"/>
<font color="Maroon" title="c4">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E2:29"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="tex_4.html#E3:29"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:29"/>
<font color="Maroon" title="c4">D1</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a>
 <b>by </b><i><a class="txt" href="tex_4.html#E5:29"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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