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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Y0</font> being    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">Y</font><br/>  for <font color="Olive" title="b2">A</font> being   <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="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">Y0</font> holds <br/>( <font color="Olive" title="b2">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  iff <font color="Olive" title="b1">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y0</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> holds <br/>( <font color="Olive" title="b1">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  iff <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> implies ( <font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  iff <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  iff <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  implies <font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:16_1"/>
<font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a> </span><br/><a NAME="E2:16_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">A</font> being   <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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> holds <br/><font color="Olive" title="b1">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:16_1"/>
<font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_2.html#D7" target="_self" title="TSP_2:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E3:16"/>
( <font color="Maroon" title="c2">Y0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  implies <font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="tsp_2.html#D7" target="_self" title="TSP_2:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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