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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</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> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c2">B</font> implies <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c2">B</font> )</span><br/>

<b>assume </b><a NAME="E1:1"/>
<font color="Maroon" title="c1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c2">B</font></span><br/>

<b>then consider </b><font color="Maroon" title="c3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:1"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E4:1"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">e</font> = <font color="Maroon" title="c3">e</font> as   <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> <b>by </b><i><a class="txt" href="jordan15.html#E3:1"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E6:1"/><i><font color="Green" title="E3">A3</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D28" title="PSCOMP_1:def.28">PSCOMP_1:def 28</a></i>;<br/>
<a NAME="E7:1"/><b>then </b><i><font color="Green" title="E4">A4</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="jordan15.html#E3:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<a NAME="E8:1"/>
<font color="Maroon" title="c4">e</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="jordan15.html#E4:1"><i><font color="Green" title="E2">A2</font></i></a>, <a class="txt" href="jordan15.html#E6:1"><i><font color="Green" title="E3">A3</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<b>hence </b><a NAME="E9:1"/>
<a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <a href="pscomp_1.html#K11" title="PSCOMP_1:func.11">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="txt" href="jordan15.html#E7:1"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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