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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">R</font>, <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b2">P</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Olive" title="b3">Q</font> &amp; <font color="Olive" title="b1">R</font> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a> <font color="Olive" title="b3">Q</font> holds <br/><font color="Olive" title="b2">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b1">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</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="c3">P</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Maroon" title="c4">Q</font> &amp; <font color="Maroon" title="c2">R</font> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a> <font color="Maroon" title="c4">Q</font> implies <font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">R</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:125"/><span class="lab"><font color="Green" title="E89">A1</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="jordan2c.html#R2" title="JORDAN2C:pred.2">is_outside_component_of</a> <font color="Maroon" title="c4">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"> (  not <font color="Maroon" title="c2">R</font> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a> <font color="Maroon" title="c4">Q</font> or <font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">R</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:125"/><span class="lab"><font color="Green" title="E90">A2</font></span>: 
<font color="Maroon" title="c2">R</font> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a> <font color="Maroon" title="c4">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="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">R</font></span><br/>

<a NAME="E3:125"/>
 <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c4">Q</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c4">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan2c.html#T24" target="_self" onmouseover="rs('jordan2c/T24')" onmouseout="rh()">Th15</a></span>;<br/>
<a NAME="E4:125"/><span class="kw">then </span>
<font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c4">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:125"><span class="lab"><font color="Green" title="E89">A1</font></span></a>, <a class="ref" href="jordan2c.html#T23" target="_self" onmouseover="rs('jordan2c/T23')" onmouseout="rh()">Th14</a>, <a class="ref" href="xboole_1.html#T63" onmouseover="rs('xboole_1/T63')" onmouseout="rh()">XBOOLE_1:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:125"/>
<font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:125"><span class="lab"><font color="Green" title="E90">A2</font></span></a>, <a class="ref" href="jordan2c.html#T22" target="_self" onmouseover="rs('jordan2c/T22')" onmouseout="rh()">Th13</a>, <a class="ref" href="xboole_1.html#T63" onmouseover="rs('xboole_1/T63')" onmouseout="rh()">XBOOLE_1:63</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/>


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