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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> ; <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">A</font>, <font color="Olive" title="b2">B</font> being 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>  st <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> holds <br/> <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Olive" title="b1">A</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Olive" title="b2">B</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> implies  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font> )</span><br/>



<a NAME="E1:126"/><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>assume </b><a NAME="E2:126"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font></span><br/>

<b>hence </b><a NAME="E3:126"/>
 <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c2">A</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="tex_4.html#K6" title="TEX_4:func.6">MaxADSspace</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:126"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="tex_4.html#E93"><i><font color="Green" title="E62">Lm2</font></i></a>, <a class="ref" href="tex_4.html#T33" target="_self" title="TEX_4:th.33">Th33</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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