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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>





<span class="kw">assume </span><a NAME="E1:31"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E2:31"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E3:31"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<div><span class="lab"><font color="Green" title="E21">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E2:31_1"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E3:31_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c6">E</font> is  <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="tex_4.html#T6" target="_self" title="TEX_4:th.6">Th6</a></span>;<br/><span class="kw">assume </span><a NAME="E4:31_1"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">hence </span><a NAME="E5:31_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E3:31"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E3:31_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:31"/>
<font color="Maroon" title="c3">D0</font> is  <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:31"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></span>;<br/>
<a NAME="E6:31"/><span class="kw">then </span>
<font color="Maroon" title="c4">D1</font> is  <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="tex_4.html#T6" target="_self" title="TEX_4:th.6">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:31"/>
<font color="Maroon" title="c4">D1</font> is  <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="tex_4.html#D7" target="_self" title="TEX_4:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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