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<b>let </b><font color="Maroon" title="c1">T</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:()"><i><font color="Red">::  thesis: </font></i></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">T</font> holds   <a href="kurato_1.html#K5" title="KURATO_1:func.5">Kurat7Set</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p5">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="kurato_1.html#K5" title="KURATO_1:func.5">Kurat7Set</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p5">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/>



 <a href="kurato_1.html#K5" title="KURATO_1:func.5">Kurat7Set</a> <font color="Maroon" title="c2">A</font> = 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T56" title="ENUMSET1:th.56">ENUMSET1:56</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p5">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p5">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T3" title="BORSUK_5:th.3">BORSUK_5:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p5">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
;<br/>
<b>hence </b><a NAME="E2:14"/>
 <a href="kurato_1.html#K5" title="KURATO_1:func.5">Kurat7Set</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p5">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ; <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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