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<span class="kw">let </span><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> ; <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">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>  holds <br/>( 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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b2">y</font></span>)</span> or  <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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b2">y</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b2">y</font></span>)</span> #) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> or  <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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) )</span><br/>



<span class="kw">assume </span><a NAME="E1:109"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>
 ; <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 <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #)</span><br/>

<a NAME="E2:109"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tex_4.html#D17" target="_self" title="TEX_4:def.17">Def17</a></span>;<br/>
<a NAME="E3:109"/>
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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tex_4.html#D17" target="_self" title="TEX_4:def.17">Def17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:109"/>
 <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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</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#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="ref" href="tex_4.html#T24" target="_self" title="TEX_4:th.24">Th24</a>, <a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</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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