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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">X0</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="tsp_2.html#NM1" title="TSP_2:NM.1">maximal_Kolmogorov_subspace</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">E</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X0</font>  st <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">E</font> holds <br/><span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b3">F</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="Olive" title="b2">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X0</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="tsp_2.html#NM1" title="TSP_2:NM.1">maximal_Kolmogorov_subspace</a> of <font color="Maroon" title="c1">X</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">E</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</font>  st <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> holds <br/><span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b2">F</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="Olive" title="b1">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</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">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</font>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">E</font> holds <br/><span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b1">F</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">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</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="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">E</font> implies <span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c4">F</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">E</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">E</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c4">F</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">E</font></span><br/>

<a NAME="E2:43"/>
 <a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>) is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_2.html#D9" target="_self" title="TSP_2:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:43"/>
<span class="p1">(<span class="default"><a href="tsp_2.html#K1" title="TSP_2:func.1">Stone-retraction</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c4">F</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">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="tsp_2.html#E37"><span class="lab"><font color="Green" title="E27">Lm6</font></span></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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