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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>;<br/>



<a NAME="E1:129"/><i><font color="Green" title="E65">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">A</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">B</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#D18" target="_self" title="TEX_4:def.18">Def19</a></i>;<br/>
<b>thus </b><a NAME="E2:129"/>
( <font color="Maroon" title="c3">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp; <font color="Maroon" title="c2">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> implies  <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> #) <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> #) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="129_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:129_1"/>
( <font color="Maroon" title="c3">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp; <font color="Maroon" title="c2">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> )
 ;<br/>

<a NAME="E2:129_1"/><b>then </b>
 <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="txt" href="tex_4.html#E1:129"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="tex_4.html#T37" target="_self" title="TEX_4:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E3:129_1"/>
 <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> #) <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> #)
 <b>by </b><i><a class="txt" href="tex_4.html#E1:129"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:129"/>
 <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> #) <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 <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> #)
 ;<br/>

<b>hence </b><a NAME="E4:129"/>
( <font color="Maroon" title="c3">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp; <font color="Maroon" title="c2">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span>)</span> )
 <b>by </b><i><a class="txt" href="tex_4.html#E1:129"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="tex_4.html#T34" target="_self" title="TEX_4:th.34">Th34</a></i>;<br/>


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