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<b>let </b><font color="Maroon" title="c1">P</font>, <font color="Maroon" title="c2">P1</font>, <font color="Maroon" title="c3">P2</font>, <font color="Maroon" title="c4">P1'</font>, <font color="Maroon" title="c5">P2'</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c6">p1</font>, <font color="Maroon" title="c7">p2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c1">P</font> <a href="topreal2.html#NR1" title="TOPREAL2:NR.1">is_simple_closed_curve</a> 
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c2">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>
 <b>and </b><br/><a NAME="E3:51"/><i><font color="Green" title="E35">A3</font></i>: 
<font color="Maroon" title="c3">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>
 <b>and </b><br/><a NAME="E4:51"/><i><font color="Green" title="E36">A4</font></i>: 
<font color="Maroon" title="c2">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P</font>
 <b>and </b><br/><a NAME="E5:51"/><i><font color="Green" title="E37">A5</font></i>: 
<font color="Maroon" title="c4">P1'</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>
 <b>and </b><br/><a NAME="E6:51"/><i><font color="Green" title="E38">A6</font></i>: 
<font color="Maroon" title="c5">P2'</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>
 <b>and </b><br/><a NAME="E7:51"/><i><font color="Green" title="E39">A7</font></i>: 
<font color="Maroon" title="c4">P1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">P2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c8">P</font> = <font color="Maroon" title="c1">P</font> as   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a> <b>by </b><i><a class="txt" href="jordan6.html#E1:51"><i><font color="Green" title="E33">A1</font></i></a></i>;<br/>
<a NAME="E9:51"/><i><font color="Green" title="E40">A8</font></i>: 
<font color="Maroon" title="c6">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">p2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="ref" href="jordan6.html#T49" target="_self" title="JORDAN6:th.49">Th49</a></i>;<br/>
<a NAME="E10:51"/><i><font color="Green" title="E41">A9</font></i>: 
( <font color="Maroon" title="c6">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c7">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1'</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></i>;<br/>
<a NAME="E11:51"/><i><font color="Green" title="E42">A10</font></i>: 
( <font color="Maroon" title="c6">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P2</font> &amp; <font color="Maroon" title="c7">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P2</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></i>;<br/>
<a NAME="E12:51"/><i><font color="Green" title="E43">A11</font></i>: 
( <font color="Maroon" title="c6">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P1</font> &amp; <font color="Maroon" title="c7">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P1</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></i>;<br/>
<a NAME="E13:51"/><i><font color="Green" title="E44">A12</font></i>: 
<font color="Maroon" title="c2">P1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E14:51"/><i><font color="Green" title="E45">A13</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<a NAME="E15:51"/>
<font color="Maroon" title="c2">P1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">Q1</font> = <font color="Maroon" title="c2">P1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">P</font></span>)</span> <b>by </b><i><a class="txt" href="jordan6.html#E13:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="jordan6.html#E14:51"><i><font color="Green" title="E45">A13</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E17:51"/><i><font color="Green" title="E46">A14</font></i>: 
<font color="Maroon" title="c3">P2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E18:51"/>
<font color="Maroon" title="c3">P2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">Q2</font> = <font color="Maroon" title="c3">P2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">P</font></span>)</span> <b>by </b><i><a class="txt" href="jordan6.html#E14:51"><i><font color="Green" title="E45">A13</font></i></a>, <a class="txt" href="jordan6.html#E17:51"><i><font color="Green" title="E46">A14</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E20:51"/><i><font color="Green" title="E47">A15</font></i>: 
<font color="Maroon" title="c4">P1'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E21:51"/>
<font color="Maroon" title="c4">P1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1'</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">Q1'</font> = <font color="Maroon" title="c4">P1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">P</font></span>)</span> <b>by </b><i><a class="txt" href="jordan6.html#E14:51"><i><font color="Green" title="E45">A13</font></i></a>, <a class="txt" href="jordan6.html#E20:51"><i><font color="Green" title="E47">A15</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E23:51"/><i><font color="Green" title="E48">A16</font></i>: 
<font color="Maroon" title="c5">P2'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E24:51"/>
<font color="Maroon" title="c5">P2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P2'</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">Q2'</font> = <font color="Maroon" title="c5">P2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">P</font></span>)</span> <b>by </b><i><a class="txt" href="jordan6.html#E14:51"><i><font color="Green" title="E45">A13</font></i></a>, <a class="txt" href="jordan6.html#E23:51"><i><font color="Green" title="E48">A16</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E26:51"/><i><font color="Green" title="E49">A17</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">P</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="jordan6.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="xboole_1.html#T42" title="XBOOLE_1:th.42">XBOOLE_1:42</a></i>;<br/>
<a NAME="E27:51"/><i><font color="Green" title="E50">A18</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">P</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="jordan6.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="xboole_1.html#T42" title="XBOOLE_1:th.42">XBOOLE_1:42</a></i>;<br/>
<a NAME="E28:51"/><b>then </b><i><font color="Green" title="E51">A19</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E29:51"/><i><font color="Green" title="E52">A20</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E30:51"/><i><font color="Green" title="E53">A21</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E31:51"/><i><font color="Green" title="E54">A22</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E32:51"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">P1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P1</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c13">R1</font> = <font color="Maroon" title="c9">Q1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">P1</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E34:51"/>
<font color="Maroon" title="c13">R1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="jordan6.html#T53" target="_self" title="JORDAN6:th.53">Th53</a></i>;<br/>
<a NAME="E35:51"/><b>then </b><i><font color="Green" title="E55">A23</font></i>: 
<font color="Maroon" title="c9">Q1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="jordan6.html#T54" target="_self" title="JORDAN6:th.54">Th54</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E36:51"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">P2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P2</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c14">R2</font> = <font color="Maroon" title="c10">Q2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">P2</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E38:51"/>
<font color="Maroon" title="c14">R2</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="jordan6.html#T53" target="_self" title="JORDAN6:th.53">Th53</a></i>;<br/>
<a NAME="E39:51"/><b>then </b><i><font color="Green" title="E56">A24</font></i>: 
<font color="Maroon" title="c10">Q2</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="jordan6.html#T54" target="_self" title="JORDAN6:th.54">Th54</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E40:51"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">P1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c15">R1'</font> = <font color="Maroon" title="c11">Q1'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">P1'</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E42:51"/>
<font color="Maroon" title="c15">R1'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="jordan6.html#T53" target="_self" title="JORDAN6:th.53">Th53</a></i>;<br/>
<a NAME="E43:51"/><b>then </b><i><font color="Green" title="E57">A25</font></i>: 
<font color="Maroon" title="c11">Q1'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="jordan6.html#T54" target="_self" title="JORDAN6:th.54">Th54</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E44:51"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">P2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">R2'</font> = <font color="Maroon" title="c12">Q2'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">P2'</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E46:51"/>
<font color="Maroon" title="c16">R2'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="ref" href="jordan6.html#T53" target="_self" title="JORDAN6:th.53">Th53</a></i>;<br/>
<a NAME="E47:51"/><b>then </b><i><font color="Green" title="E58">A26</font></i>: 
<font color="Maroon" title="c12">Q2'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan6.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="jordan6.html#T54" target="_self" title="JORDAN6:th.54">Th54</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E48:51"/><i><font color="Green" title="E59">A27</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_1"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E2:51_1"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E12:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E49:51"/><i><font color="Green" title="E60">A28</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_2"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E2:51_2"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E11:51"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E50:51"/><i><font color="Green" title="E61">A29</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_3"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E2:51_3"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51"><i><font color="Green" title="E41">A9</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E51:51"/><i><font color="Green" title="E62">A30</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_4"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<a NAME="E2:51_4"/><b>then </b>
( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p1</font> or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p2</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:51_4"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="ref" href="topreal1.html#T4" title="TOPREAL1:th.4">TOPREAL1:4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E52:51"/><i><font color="Green" title="E63">A31</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P1</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E48:51"><i><font color="Green" title="E59">A27</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E53:51"/><i><font color="Green" title="E64">A32</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E49:51"><i><font color="Green" title="E60">A28</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E54:51"/><i><font color="Green" title="E65">A33</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E50:51"><i><font color="Green" title="E61">A29</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E55:51"/><i><font color="Green" title="E66">A34</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E51:51"><i><font color="Green" title="E62">A30</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5"/><i><font color="Green" title="E67">A35</font></i>: 
(  not <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> or  not <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_5_1_1"/>
( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">P2'</font> or <font color="Maroon" title="c3">P2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P1'</font> )
 </span><b>by </b><i><a class="txt" href="jordan6.html#E1:51_5"><i><font color="Green" title="E67">A35</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_1"><b>case </b></a><a NAME="E1:51_5_1_1_1"/><i><font color="Green" title="E68">A36</font></i>: 
<font color="Maroon" title="c2">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">P2'</font>
 ;<br/><div class="add"><div><i><font color="Green" title="E69">A37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_1_1"/><i><font color="Green" title="E70">A38</font></i>: 
( <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c9">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><a NAME="E2:51_5_1_1_1_1"/><b>then </b><i><font color="Green" title="E71">A39</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/><a NAME="E3:51_5_1_1_1_1"/>
<font color="Maroon" title="c12">Q2'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_1_1"><i><font color="Green" title="E70">A38</font></i></a>, <a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/><b>hence </b><a NAME="E4:51_5_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E52:51"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="jordan6.html#E55:51"><i><font color="Green" title="E66">A34</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_1"><i><font color="Green" title="E68">A36</font></i></a>, <a class="txt" href="jordan6.html#E2:51_5_1_1_1_1"><i><font color="Green" title="E71">A39</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_5_1_1_1_2_1"/>
( <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c9">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span><b>by </b><i><a class="txt" href="jordan6.html#E2:51_5_1_1_1"><i><font color="Green" title="E69">A37</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_1_2_1_1"><b>case </b></a><a NAME="E1:51_5_1_1_1_2_1_1"/><i><font color="Green" title="E70">A40</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c17">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c12">Q2'</font>;<br/><a NAME="E3:51_5_1_1_1_2_1_1"/><i><font color="Green" title="E71">A41</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_1"><i><font color="Green" title="E70">A40</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:51_5_1_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E72">A42</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:51_5_1_1_1_2_1_1"/>
not <font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_1"><i><font color="Green" title="E70">A40</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:51_5_1_1_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E4:51_5_1_1_1_2_1_1"><i><font color="Green" title="E72">A42</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:51_5_1_1_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">Q1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="jordan6.html#E3:51_5_1_1_1_2_1_1"><i><font color="Green" title="E71">A41</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:51_5_1_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E73">A43</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c10">Q2</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c11">Q1'</font>
 ;<br/><a NAME="E2:51_5_1_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">Q1'</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="jordan6.html#E35:51"><i><font color="Green" title="E55">A23</font></i></a>, <a class="txt" href="jordan6.html#E39:51"><i><font color="Green" title="E56">A24</font></i></a>, <a class="txt" href="jordan6.html#E43:51"><i><font color="Green" title="E57">A25</font></i></a>, <a class="txt" href="jordan6.html#E8:51_5_1_1_1_2_1_1"><i><font color="Green" title="E73">A43</font></i></a>, <a class="ref" href="jordan1.html#T7" title="JORDAN1:th.7">JORDAN1:7</a></i>;<br/><b>hence </b><a NAME="E3:51_5_1_1_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E9:51"><i><font color="Green" title="E40">A8</font></i></a>, <a class="txt" href="jordan6.html#E12:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="jordan6.html#E13:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E28:51"><i><font color="Green" title="E51">A19</font></i></a>, <a class="ref" href="jordan6.html#T60" target="_self" title="JORDAN6:th.60">Th60</a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/></div><b>end;</b></div><a NAME="E10:51_5_1_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E74">A44</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">Q1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E11:51_5_1_1_1_2_1_1"/><i><font color="Green" title="E75">A45</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_1_2_1_1_2"/><i><font color="Green" title="E76">A46</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 ;<br/>

<a NAME="E2:51_5_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_1_2_1_1_2"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_1_2_1_1"><i><font color="Green" title="E74">A44</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_1_2"><i><font color="Green" title="E76">A46</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:51_5_1_1_1_2_1_1"/>
<font color="Maroon" title="c11">Q1'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">Q1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_1_2_1_1_3"/><i><font color="Green" title="E76">A47</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 ;<br/>

<a NAME="E2:51_5_1_1_1_2_1_1_3"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_1_2_1_1_3"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_1_2_1_1_3"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_1_2_1_1"><i><font color="Green" title="E74">A44</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_1_3"><i><font color="Green" title="E76">A47</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E13:51_5_1_1_1_2_1_1"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 <b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="jordan6.html#E52:51"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="jordan6.html#E53:51"><i><font color="Green" title="E64">A32</font></i></a>, <a class="txt" href="jordan6.html#E54:51"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="jordan6.html#E55:51"><i><font color="Green" title="E66">A34</font></i></a>, <a class="txt" href="jordan6.html#E11:51_5_1_1_1_2_1_1"><i><font color="Green" title="E75">A45</font></i></a>, <a class="ref" href="jordan6.html#T59" target="_self" title="JORDAN6:th.59">Th59</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_1_2_1_2"><b>case </b></a><a NAME="E1:51_5_1_1_1_2_1_2"/><i><font color="Green" title="E70">A48</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c9">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c17">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c9">Q1</font>;<br/><a NAME="E3:51_5_1_1_1_2_1_2"/><i><font color="Green" title="E71">A49</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_2"><i><font color="Green" title="E70">A48</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:51_5_1_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E72">A50</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:51_5_1_1_1_2_1_2"/>
not <font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_2"><i><font color="Green" title="E70">A48</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:51_5_1_1_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E4:51_5_1_1_1_2_1_2"><i><font color="Green" title="E72">A50</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:51_5_1_1_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="jordan6.html#E3:51_5_1_1_1_2_1_2"><i><font color="Green" title="E71">A49</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:51_5_1_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E73">A51</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_1_2_1_2_1"/>
<font color="Maroon" title="c11">Q1'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c10">Q2</font>
 ;<br/><a NAME="E2:51_5_1_1_1_2_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">Q1'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="jordan6.html#E39:51"><i><font color="Green" title="E56">A24</font></i></a>, <a class="txt" href="jordan6.html#E43:51"><i><font color="Green" title="E57">A25</font></i></a>, <a class="txt" href="jordan6.html#E47:51"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="jordan6.html#E8:51_5_1_1_1_2_1_2"><i><font color="Green" title="E73">A51</font></i></a>, <a class="ref" href="jordan1.html#T7" title="JORDAN1:th.7">JORDAN1:7</a></i>;<br/><b>hence </b><a NAME="E3:51_5_1_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E9:51"><i><font color="Green" title="E40">A8</font></i></a>, <a class="txt" href="jordan6.html#E12:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="jordan6.html#E13:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="txt" href="jordan6.html#E31:51"><i><font color="Green" title="E54">A22</font></i></a>, <a class="ref" href="jordan6.html#T60" target="_self" title="JORDAN6:th.60">Th60</a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/></div><b>end;</b></div><a NAME="E10:51_5_1_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E74">A52</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E11:51_5_1_1_1_2_1_2"/><i><font color="Green" title="E75">A53</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">Q1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_1_2_1_2_2"/><i><font color="Green" title="E76">A54</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 ;<br/>

<a NAME="E2:51_5_1_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_1_2_1_2_2"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_1_2_1_2_2"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_1_2_1_2"><i><font color="Green" title="E74">A52</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_2_2"><i><font color="Green" title="E76">A54</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:51_5_1_1_1_2_1_2"/>
<font color="Maroon" title="c10">Q2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_1_2_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_1_2_1_2_3"/><i><font color="Green" title="E76">A55</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 ;<br/>

<a NAME="E2:51_5_1_1_1_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_1_2_1_2_3"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_1_2_1_2_3"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_1_2_1_2"><i><font color="Green" title="E74">A52</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_1_2_1_2_3"><i><font color="Green" title="E76">A55</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E13:51_5_1_1_1_2_1_2"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 <b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="jordan6.html#E52:51"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="jordan6.html#E53:51"><i><font color="Green" title="E64">A32</font></i></a>, <a class="txt" href="jordan6.html#E54:51"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="jordan6.html#E55:51"><i><font color="Green" title="E66">A34</font></i></a>, <a class="txt" href="jordan6.html#E11:51_5_1_1_1_2_1_2"><i><font color="Green" title="E75">A53</font></i></a>, <a class="ref" href="jordan6.html#T59" target="_self" title="JORDAN6:th.59">Th59</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:51_5_1_1_1"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_2"><b>case </b></a><a NAME="E1:51_5_1_1_2"/><i><font color="Green" title="E68">A56</font></i>: 
<font color="Maroon" title="c3">P2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P1'</font>
 ;<br/><div class="add"><div><i><font color="Green" title="E69">A57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_2_1"/><i><font color="Green" title="E70">A58</font></i>: 
( <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c11">Q1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><a NAME="E2:51_5_1_1_2_1"/><b>then </b><i><font color="Green" title="E71">A59</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/><a NAME="E3:51_5_1_1_2_1"/>
<font color="Maroon" title="c11">Q1'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_2_1"><i><font color="Green" title="E70">A58</font></i></a>, <a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/><b>hence </b><a NAME="E4:51_5_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E53:51"><i><font color="Green" title="E64">A32</font></i></a>, <a class="txt" href="jordan6.html#E54:51"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_2"><i><font color="Green" title="E68">A56</font></i></a>, <a class="txt" href="jordan6.html#E2:51_5_1_1_2_1"><i><font color="Green" title="E71">A59</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_5_1_1_2_2_1"/>
( <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c11">Q1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span><b>by </b><i><a class="txt" href="jordan6.html#E2:51_5_1_1_2"><i><font color="Green" title="E69">A57</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_2_2_1_1"><b>case </b></a><a NAME="E1:51_5_1_1_2_2_1_1"/><i><font color="Green" title="E70">A60</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c11">Q1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c17">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c11">Q1'</font>;<br/><a NAME="E3:51_5_1_1_2_2_1_1"/><i><font color="Green" title="E71">A61</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_1"><i><font color="Green" title="E70">A60</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:51_5_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E72">A62</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:51_5_1_1_2_2_1_1"/>
not <font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_1"><i><font color="Green" title="E70">A60</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:51_5_1_1_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E4:51_5_1_1_2_2_1_1"><i><font color="Green" title="E72">A62</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:51_5_1_1_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="jordan6.html#E3:51_5_1_1_2_2_1_1"><i><font color="Green" title="E71">A61</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:51_5_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E73">A63</font></i>: 
<font color="Maroon" title="c10">Q2</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c12">Q2'</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_2_2_1_1_1"/>
<font color="Maroon" title="c9">Q1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c12">Q2'</font>
 ;<br/><a NAME="E2:51_5_1_1_2_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="jordan6.html#E35:51"><i><font color="Green" title="E55">A23</font></i></a>, <a class="txt" href="jordan6.html#E39:51"><i><font color="Green" title="E56">A24</font></i></a>, <a class="txt" href="jordan6.html#E47:51"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="jordan6.html#E8:51_5_1_1_2_2_1_1"><i><font color="Green" title="E73">A63</font></i></a>, <a class="ref" href="jordan1.html#T7" title="JORDAN1:th.7">JORDAN1:7</a></i>;<br/><b>hence </b><a NAME="E3:51_5_1_1_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E9:51"><i><font color="Green" title="E40">A8</font></i></a>, <a class="txt" href="jordan6.html#E12:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="jordan6.html#E13:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E29:51"><i><font color="Green" title="E52">A20</font></i></a>, <a class="ref" href="jordan6.html#T60" target="_self" title="JORDAN6:th.60">Th60</a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/></div><b>end;</b></div><a NAME="E10:51_5_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E74">A64</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c12">Q2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E11:51_5_1_1_2_2_1_1"/><i><font color="Green" title="E75">A65</font></i>: 
<font color="Maroon" title="c9">Q1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_2_2_1_1_2"/><i><font color="Green" title="E76">A66</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 ;<br/>

<a NAME="E2:51_5_1_1_2_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_2_2_1_1_2"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_2_2_1_1_2"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_2_2_1_1"><i><font color="Green" title="E74">A64</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_1_2"><i><font color="Green" title="E76">A66</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:51_5_1_1_2_2_1_1"/>
<font color="Maroon" title="c12">Q2'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">Q2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_2_2_1_1_3"/><i><font color="Green" title="E76">A67</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 ;<br/>

<a NAME="E2:51_5_1_1_2_2_1_1_3"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_2_2_1_1_3"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_2_2_1_1_3"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_2_2_1_1"><i><font color="Green" title="E74">A64</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_1_3"><i><font color="Green" title="E76">A67</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E13:51_5_1_1_2_2_1_1"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 <b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="jordan6.html#E52:51"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="jordan6.html#E53:51"><i><font color="Green" title="E64">A32</font></i></a>, <a class="txt" href="jordan6.html#E54:51"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="jordan6.html#E55:51"><i><font color="Green" title="E66">A34</font></i></a>, <a class="txt" href="jordan6.html#E11:51_5_1_1_2_2_1_1"><i><font color="Green" title="E75">A65</font></i></a>, <a class="ref" href="jordan6.html#T59" target="_self" title="JORDAN6:th.59">Th59</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_5_1_1_2_2_1_2"><b>case </b></a><a NAME="E1:51_5_1_1_2_2_1_2"/><i><font color="Green" title="E70">A68</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c10">Q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c17">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c10">Q2</font>;<br/><a NAME="E3:51_5_1_1_2_2_1_2"/><i><font color="Green" title="E71">A69</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_2"><i><font color="Green" title="E70">A68</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:51_5_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E72">A70</font></i>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:51_5_1_1_2_2_1_2"/>
not <font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_2"><i><font color="Green" title="E70">A68</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:51_5_1_1_2_2_1_2"/><b>then </b>
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E4:51_5_1_1_2_2_1_2"><i><font color="Green" title="E72">A70</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:51_5_1_1_2_2_1_2"/><b>then </b>
<font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="jordan6.html#E3:51_5_1_1_2_2_1_2"><i><font color="Green" title="E71">A69</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:51_5_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E73">A71</font></i>: 
<font color="Maroon" title="c11">Q1'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c9">Q1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_5_1_1_2_2_1_2_1"/>
<font color="Maroon" title="c12">Q2'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c9">Q1</font>
 ;<br/><a NAME="E2:51_5_1_1_2_2_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">Q1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="jordan6.html#E35:51"><i><font color="Green" title="E55">A23</font></i></a>, <a class="txt" href="jordan6.html#E43:51"><i><font color="Green" title="E57">A25</font></i></a>, <a class="txt" href="jordan6.html#E47:51"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="jordan6.html#E8:51_5_1_1_2_2_1_2"><i><font color="Green" title="E73">A71</font></i></a>, <a class="ref" href="jordan1.html#T7" title="JORDAN1:th.7">JORDAN1:7</a></i>;<br/><b>hence </b><a NAME="E3:51_5_1_1_2_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan6.html#E9:51"><i><font color="Green" title="E40">A8</font></i></a>, <a class="txt" href="jordan6.html#E12:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="jordan6.html#E13:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="txt" href="jordan6.html#E30:51"><i><font color="Green" title="E53">A21</font></i></a>, <a class="ref" href="jordan6.html#T60" target="_self" title="JORDAN6:th.60">Th60</a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/></div><b>end;</b></div><a NAME="E10:51_5_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E74">A72</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E11:51_5_1_1_2_2_1_2"/><i><font color="Green" title="E75">A73</font></i>: 
<font color="Maroon" title="c12">Q2'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">Q2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_2_2_1_2_2"/><i><font color="Green" title="E76">A74</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font>
 ;<br/>

<a NAME="E2:51_5_1_1_2_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">Q1'</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_2_2_1_2_2"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font> )
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_2_2_1_2_2"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Q2</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_2_2_1_2"><i><font color="Green" title="E74">A72</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_2_2"><i><font color="Green" title="E76">A74</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:51_5_1_1_2_2_1_2"/>
<font color="Maroon" title="c9">Q1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5_1_1_2_2_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_5_1_1_2_2_1_2_3"/><i><font color="Green" title="E76">A75</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q1</font>
 ;<br/>

<a NAME="E2:51_5_1_1_2_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">Q2'</font>
 
<b>by </b><i><a class="txt" href="jordan6.html#E26:51"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="jordan6.html#E27:51"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:51_5_1_1_2_2_1_2_3"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Q2'</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:51_5_1_1_2_2_1_2_3"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Q1'</font>
 <b>by </b><i><a class="txt" href="jordan6.html#E10:51_5_1_1_2_2_1_2"><i><font color="Green" title="E74">A72</font></i></a>, <a class="txt" href="jordan6.html#E1:51_5_1_1_2_2_1_2_3"><i><font color="Green" title="E76">A75</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E13:51_5_1_1_2_2_1_2"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 <b>by </b><i><a class="txt" href="jordan6.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="jordan6.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="jordan6.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="jordan6.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="jordan6.html#E52:51"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="jordan6.html#E53:51"><i><font color="Green" title="E64">A32</font></i></a>, <a class="txt" href="jordan6.html#E54:51"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="jordan6.html#E55:51"><i><font color="Green" title="E66">A34</font></i></a>, <a class="txt" href="jordan6.html#E11:51_5_1_1_2_2_1_2"><i><font color="Green" title="E75">A73</font></i></a>, <a class="ref" href="jordan6.html#T59" target="_self" title="JORDAN6:th.59">Th59</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:51_5_1_1_2"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:51_5"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E57:51"/>
( ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> ) or ( <font color="Maroon" title="c2">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P2'</font> &amp; <font color="Maroon" title="c3">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1'</font> ) )
 ;<br/>


</div>
