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<span class="kw">let </span><font color="Maroon" title="c1">FT</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font><br/>  for <font color="Olive" title="b3">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Olive" title="b3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  &amp; <font color="Olive" title="b1">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  &amp; <font color="Olive" title="b2">C</font> <a href="fintopo6.html#R2" title="FINTOPO6:pred.2">is_a_component_of</a> <font color="Olive" title="b3">D</font> holds <br/><span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  &amp; <font color="Maroon" title="c3">C</font> <a href="fintopo6.html#R2" title="FINTOPO6:pred.2">is_a_component_of</a> <font color="Olive" title="b1">D</font> holds <br/><span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  &amp; <font color="Maroon" title="c3">C</font> <a href="fintopo6.html#R2" title="FINTOPO6:pred.2">is_a_component_of</a> <font color="Maroon" title="c4">D</font> implies <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:52"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
( <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  )
 <span class="kw">and </span><br/><a NAME="E2:52"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E3:52"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c1">FT</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a> 
 <span class="kw">and </span><br/><a NAME="E4:52"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">and </span><br/><a NAME="E5:52"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<font color="Maroon" title="c3">C</font> <a href="fintopo6.html#R2" title="FINTOPO6:pred.2">is_a_component_of</a> <font color="Maroon" title="c4">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">C1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:52"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
<font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">and </span><br/><a NAME="E8:52"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
<font color="Maroon" title="c5">C1</font> <a href="fintopo6.html#R1" title="FINTOPO6:pred.1">is_a_component_of</a> <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52"><span class="lab"><font color="Green" title="E28">A5</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">C2</font> = <font color="Maroon" title="c5">C1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a></span>;<br/>
<a NAME="E10:52"/>
<font color="Maroon" title="c5">C1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
;<br/>
<a NAME="E11:52"/><span class="kw">then </span>
<font color="Maroon" title="c5">C1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<a NAME="E12:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C2</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T12" onmouseover="rs('subset_1/T12')" onmouseout="rh()">SUBSET_1:12</a></span>;<br/>
<a NAME="E13:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A9</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C2</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T3" onmouseover="rs('pre_topc/T3')" onmouseout="rh()">PRE_TOPC:3</a></span>;<br/>
<a NAME="E14:52"/><span class="lab"><font color="Green" title="E33">A10</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c6">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:52"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="ref" href="pre_topc.html#T3" onmouseover="rs('pre_topc/T3')" onmouseout="rh()">PRE_TOPC:3</a></span>;<br/>
<a NAME="E15:52"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
<font color="Maroon" title="c5">C1</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52"><span class="lab"><font color="Green" title="E30">A7</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="52_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">Q</font> &amp; <font color="Olive" title="b1">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">Q</font> &amp; <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font> <a href="fintopo4.html#R1" title="FINTOPO4:pred.1">are_separated</a>  &amp;  not <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> holds <br/><font color="Olive" title="b2">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font></span></a><div class="add"><a NAME="E1:52_1"/>
<font color="Maroon" title="c2">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:52"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="ref" href="subset_1.html#T23" onmouseover="rs('subset_1/T23')" onmouseout="rh()">SUBSET_1:23</a></span>;<br/><a NAME="E2:52_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A12</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><span class="kw">let </span><font color="Maroon" title="c7">P</font>, <font color="Maroon" title="c8">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> &amp; <font color="Maroon" title="c7">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">Q</font> &amp; <font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c8">Q</font> <a href="fintopo4.html#R1" title="FINTOPO4:pred.1">are_separated</a>  &amp;  not <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> implies <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:52_1"/><span class="lab"><font color="Green" title="E36">A13</font></span>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font>
 <span class="kw">and </span><br/><a NAME="E4:52_1"/><span class="lab"><font color="Green" title="E37">A14</font></span>: 
<font color="Maroon" title="c7">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">Q</font>
 <span class="kw">and </span><br/><a NAME="E5:52_1"/><span class="lab"><font color="Green" title="E38">A15</font></span>: 
<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c8">Q</font> <a href="fintopo4.html#R1" title="FINTOPO4:pred.1">are_separated</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> or <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )</span><br/><a NAME="E6:52_1"/><span class="lab"><font color="Green" title="E39">A16</font></span>: 
<font color="Maroon" title="c3">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E15:52"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="ref" href="fintopo6.html#T38" target="_self" onmouseover="rs('fintopo6/T38')" onmouseout="rh()">Th37</a></span>;<br/><div><span class="lab"><font color="Green" title="E40">A17</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="52_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Q</font> implies <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_1"/><span class="lab"><font color="Green" title="E41">A18</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Q</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font></span><br/><a NAME="E2:52_1_1"/>
<font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="ref" href="subset_1.html#T23" onmouseover="rs('subset_1/T23')" onmouseout="rh()">SUBSET_1:23</a></span>;<br/><a NAME="E3:52_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c8">Q</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Q</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E41">A18</font></span></a>, <a class="ref" href="xboole_1.html#T27" onmouseover="rs('xboole_1/T27')" onmouseout="rh()">XBOOLE_1:27</a>, <a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><a NAME="E4:52_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A19</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">P</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T23" onmouseover="rs('xboole_1/T23')" onmouseout="rh()">XBOOLE_1:23</a></span>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E2:52_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E4:52_1_1"><span class="lab"><font color="Green" title="E42">A19</font></span></a>, <a class="ref" href="xboole_1.html#T3" onmouseover="rs('xboole_1/T3')" onmouseout="rh()">XBOOLE_1:3</a></span>
;<br/><a NAME="E6:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">A</font>
 ;<br/><a NAME="E7:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T23" onmouseover="rs('subset_1/T23')" onmouseout="rh()">SUBSET_1:23</a></span>;<br/><a NAME="E8:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">C1P1</font> = <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span> ;<br/><a NAME="E10:52_1_1"/>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">P</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E3:52"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E3:52_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="txt" href="#E5:52_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E6:52_1"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="ref" href="fintopo6.html#T37" target="_self" onmouseover="rs('fintopo6/T37')" onmouseout="rh()">Th36</a></span>;<br/><a NAME="E11:52_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A20</font></span>: 
<font color="Maroon" title="c9">C1P1</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#T38" target="_self" onmouseover="rs('fintopo6/T38')" onmouseout="rh()">Th37</a></span>;<br/><a NAME="E12:52_1_1"/>
<font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">C1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><a NAME="E13:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">C1P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E8:52"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E11:52_1_1"><span class="lab"><font color="Green" title="E43">A20</font></span></a></span>;<br/><a NAME="E14:52_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A21</font></span>: 
<font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><a NAME="E15:52_1_1"/>
<font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><a NAME="E16:52_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">C</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:52_1_1"><span class="lab"><font color="Green" title="E44">A21</font></span></a>, <a class="ref" href="xboole_1.html#T19" onmouseover="rs('xboole_1/T19')" onmouseout="rh()">XBOOLE_1:19</a>, <a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><a NAME="E17:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><span class="kw">hence </span><a NAME="E18:52_1_1"/>
<font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T3" onmouseover="rs('xboole_1/T3')" onmouseout="rh()">XBOOLE_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E8:52_1"/><span class="lab"><font color="Green" title="E41">A22</font></span>: 
<font color="Maroon" title="c7">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><a NAME="E9:52_1"/><span class="lab"><font color="Green" title="E42">A23</font></span>: 
<font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="52_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> implies <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_2"/><span class="lab"><font color="Green" title="E43">A24</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font></span><br/><a NAME="E2:52_1_2"/>
<font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="ref" href="subset_1.html#T23" onmouseover="rs('subset_1/T23')" onmouseout="rh()">SUBSET_1:23</a></span>;<br/><a NAME="E3:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_2"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="ref" href="xboole_1.html#T27" onmouseover="rs('xboole_1/T27')" onmouseout="rh()">XBOOLE_1:27</a></span>;<br/><a NAME="E4:52_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A25</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52_1"><span class="lab"><font color="Green" title="E41">A22</font></span></a></span>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T23" onmouseover="rs('xboole_1/T23')" onmouseout="rh()">XBOOLE_1:23</a></span>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E2:52_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E4:52_1_2"><span class="lab"><font color="Green" title="E44">A25</font></span></a>, <a class="ref" href="xboole_1.html#T3" onmouseover="rs('xboole_1/T3')" onmouseout="rh()">XBOOLE_1:3</a></span>
;<br/><a NAME="E6:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">A</font>
 ;<br/><a NAME="E7:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T23" onmouseover="rs('subset_1/T23')" onmouseout="rh()">SUBSET_1:23</a></span>;<br/><a NAME="E8:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">C1Q1</font> = <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c4">D</font></span>)</span> ;<br/><a NAME="E10:52_1_2"/>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Q</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E3:52"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E3:52_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="txt" href="#E5:52_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E6:52_1"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="ref" href="fintopo6.html#T37" target="_self" onmouseover="rs('fintopo6/T37')" onmouseout="rh()">Th36</a></span>;<br/><a NAME="E11:52_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A26</font></span>: 
<font color="Maroon" title="c9">C1Q1</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#T38" target="_self" onmouseover="rs('fintopo6/T38')" onmouseout="rh()">Th37</a></span>;<br/><a NAME="E12:52_1_2"/>
<font color="Maroon" title="c5">C1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">C1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c8">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><a NAME="E13:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">C1Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E8:52"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E11:52_1_2"><span class="lab"><font color="Green" title="E45">A26</font></span></a></span>;<br/><a NAME="E14:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/><a NAME="E15:52_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c3">C</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:52_1"><span class="lab"><font color="Green" title="E42">A23</font></span></a>, <a class="ref" href="xboole_1.html#T19" onmouseover="rs('xboole_1/T19')" onmouseout="rh()">XBOOLE_1:19</a>, <a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><a NAME="E16:52_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><span class="kw">hence </span><a NAME="E17:52_1_2"/>
<font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T3" onmouseover="rs('xboole_1/T3')" onmouseout="rh()">XBOOLE_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E11:52_1"/>
( <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> or <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E4:52"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E7:52"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E14:52"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="txt" href="#E3:52_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="txt" href="#E5:52_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E7:52_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a>, <a class="ref" href="fintopo6.html#T33" target="_self" onmouseover="rs('fintopo6/T33')" onmouseout="rh()">Th32</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E17:52"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="fintopo6.html#T7" target="_self" onmouseover="rs('fintopo6/T7')" onmouseout="rh()">Th6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
