<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:160_1_1"/>
<font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> is <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> is <a href="coh_sp.html#V1" title="COH_SP:attr.1">binary_complete</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</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="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> or  not <font color="Maroon" title="c4">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> )</span><br/>

<b>assume </b><a NAME="E1:160_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> )</span><br/>

<b>then consider </b><font color="Maroon" title="c5">a1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c6">a2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_1"/><i><font color="Green" title="E89">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T97" target="_self" title="COHSP_1:th.97">Th97</a></i>;<br/>
<b>assume </b><a NAME="E4:160_1_1_1"/>
<font color="Maroon" title="c4">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font></span><br/>

<a NAME="E5:160_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E3:160_1_1_1"><i><font color="Green" title="E89">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:160_1_1_1"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T97" target="_self" title="COHSP_1:th.97">Th97</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">A</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="cohsp_1.html#D1" target="_self" title="COHSP_1:def.1">COHSP_1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> holds <br/><font color="Olive" title="b1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> ) implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> )</span><br/>

<b>assume </b><a NAME="E2:160_1_1"/><i><font color="Green" title="E89">A2</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> holds <br/><font color="Olive" title="b1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font></span><br/>

<b>set </b><font color="Maroon" title="c4">A1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c5">A2</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">b1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  implies <font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> )</span><br/><b>assume </b><a NAME="E1:160_1_1_2"/>
<font color="Maroon" title="c6">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </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="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  implies <font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> )</span><br/><b>then consider </b><font color="Maroon" title="c8">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_2"/><i><font color="Green" title="E90">A3</font></i>: 
( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c8">a</font> &amp; <font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><b>assume </b><a NAME="E4:160_1_1_2"/>
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </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="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font></span><br/><b>then consider </b><font color="Maroon" title="c9">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E6:160_1_1_2"/><i><font color="Green" title="E91">A4</font></i>: 
( <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c9">b</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><a NAME="E7:160_1_1_2"/>
<font color="Maroon" title="c8">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="#E2:160_1_1"><i><font color="Green" title="E89">A2</font></i></a>, <a class="txt" href="#E3:160_1_1_2"><i><font color="Green" title="E90">A3</font></i></a>, <a class="txt" href="#E6:160_1_1_2"><i><font color="Green" title="E91">A4</font></i></a></i>;<br/><a NAME="E8:160_1_1_2"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T98" target="_self" title="COHSP_1:th.98">Th98</a></i>;<br/><b>hence </b><a NAME="E9:160_1_1_2"/>
<font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font>
 <b>by </b><i><a class="txt" href="#E3:160_1_1_2"><i><font color="Green" title="E90">A3</font></i></a>, <a class="txt" href="#E6:160_1_1_2"><i><font color="Green" title="E91">A4</font></i></a>, <a class="ref" href="funct_5.html#T6" title="FUNCT_5:th.6">FUNCT_5:6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E4:160_1_1"/><b>then </b><i><font color="Green" title="E90">A5</font></i>: 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D1" target="_self" title="COHSP_1:def.1">Def1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">b1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  implies <font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font> )</span><br/><b>assume </b><a NAME="E1:160_1_1_3"/>
<font color="Maroon" title="c6">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </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="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  implies <font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font> )</span><br/><b>then consider </b><font color="Maroon" title="c8">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_3"/><i><font color="Green" title="E91">A6</font></i>: 
( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c8">a</font> &amp; <font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><b>assume </b><a NAME="E4:160_1_1_3"/>
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </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="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font></span><br/><b>then consider </b><font color="Maroon" title="c9">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E6:160_1_1_3"/><i><font color="Green" title="E92">A7</font></i>: 
( <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c9">b</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><a NAME="E7:160_1_1_3"/>
<font color="Maroon" title="c8">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="#E2:160_1_1"><i><font color="Green" title="E89">A2</font></i></a>, <a class="txt" href="#E3:160_1_1_3"><i><font color="Green" title="E91">A6</font></i></a>, <a class="txt" href="#E6:160_1_1_3"><i><font color="Green" title="E92">A7</font></i></a></i>;<br/><a NAME="E8:160_1_1_3"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T98" target="_self" title="COHSP_1:th.98">Th98</a></i>;<br/><b>hence </b><a NAME="E9:160_1_1_3"/>
<font color="Maroon" title="c6">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="#E3:160_1_1_3"><i><font color="Green" title="E91">A6</font></i></a>, <a class="txt" href="#E6:160_1_1_3"><i><font color="Green" title="E92">A7</font></i></a>, <a class="ref" href="funct_5.html#T6" title="FUNCT_5:th.6">FUNCT_5:6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E6:160_1_1"/><b>then </b><i><font color="Green" title="E91">A8</font></i>: 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D1" target="_self" title="COHSP_1:def.1">Def1</a></i>;<br/>
<a NAME="E7:160_1_1"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:160_1_1_4"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:160_1_1_4"/><i><font color="Green" title="E92">A9</font></i>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">a</font> &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<a NAME="E4:160_1_1_4"/>
<font color="Maroon" title="c7">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 
<b>by </b><i><a class="txt" href="#E2:160_1_1"><i><font color="Green" title="E89">A2</font></i></a>, <a class="txt" href="#E3:160_1_1_4"><i><font color="Green" title="E92">A9</font></i></a></i>;<br/>
<a NAME="E5:160_1_1_4"/><b>then </b>
( <font color="Maroon" title="c7">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c7">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c7">a</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  )
 
<b>by </b><i><a class="txt" href="#E3:160_1_1_4"><i><font color="Green" title="E92">A9</font></i></a>, <a class="ref" href="cohsp_1.html#T98" target="_self" title="COHSP_1:th.98">Th98</a></i>;<br/>
<a NAME="E6:160_1_1_4"/><b>then </b><i><font color="Green" title="E93">A10</font></i>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c7">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c7">a</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c7">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c7">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  )
 
<b>by </b><i><a class="txt" href="#E3:160_1_1_4"><i><font color="Green" title="E92">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E7:160_1_1_4"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c7">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c7">a</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<b>hence </b><a NAME="E8:160_1_1_4"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="#E6:160_1_1_4"><i><font color="Green" title="E93">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:160_1_1"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> <a href="cohsp_1.html#K17" title="COHSP_1:func.17">[*]</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="#E4:160_1_1"><i><font color="Green" title="E90">A5</font></i></a>, <a class="txt" href="#E6:160_1_1"><i><font color="Green" title="E91">A8</font></i></a>, <a class="ref" href="cohsp_1.html#T97" target="_self" title="COHSP_1:th.97">Th97</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
