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

<span class="kw">set </span><font color="Maroon" title="c2">FV</font> = <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">TT</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">TT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>, <font color="Olive" title="b3">f</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Maroon" title="c1">X</font> : ( (  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b3">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font></span>)</span> &amp; (  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">T</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">TT</font> ) ) </span> } </span> ;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="28_1_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">  ex <font color="Olive" title="b1">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">T</font>,<font color="Olive" title="b3">TT</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b4">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b2">T</font>, <font color="Olive" title="b3">TT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>, <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Maroon" title="c1">X</font> : ( (  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b3">TT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b4">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b3">TT</font></span>)</span> &amp; (  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">T</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">TT</font> ) ) </span> } </span> </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> =  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">X</font> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> ;<br/><a NAME="E2:28_1_1_1"/>
<font color="Maroon" title="c3">A</font> is   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T2" target="_self" onmouseover="rs('coh_sp/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E3:28_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">xx</font> where <font color="Olive" title="b1">xx</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> : <font color="Olive" title="b1">xx</font> is   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a> </span> } </span> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">A</font> = <font color="Maroon" title="c3">A</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font> ;<br/><span class="kw">set </span><font color="Maroon" title="c5">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font></span>)</span>;<br/><span class="kw">take </span><font color="Maroon" title="c6">m</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c4">A</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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"> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">TT</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">TT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>, <font color="Olive" title="b3">f</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Maroon" title="c1">X</font> : ( (  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b3">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font></span>)</span> &amp; (  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">T</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">TT</font> ) ) </span> } </span> </span><br/><a NAME="E5:28_1_1_1"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
(  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</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">reconsider </span><font color="Maroon" title="c7">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T17" target="_self" onmouseover="rs('coh_sp/T17')" onmouseout="rh()">Th17</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="28_1_1_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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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"> ( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font> implies <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font> )</span><br/><span class="kw">assume </span><a NAME="E1:28_1_1_1_1"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font></span><br/><a NAME="E2:28_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T16" target="_self" onmouseover="rs('coh_sp/T16')" onmouseout="rh()">Th16</a></span>;<br/><a NAME="E3:28_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>;<br/><a NAME="E4:28_1_1_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_1_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="coh_sp.html#T16" target="_self" onmouseover="rs('coh_sp/T16')" onmouseout="rh()">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E5:28_1_1_1_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_1_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:28_1_1_1_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</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="E8:28_1_1_1"/>
<font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">TT</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">TT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>, <font color="Olive" title="b3">f</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Maroon" title="c1">X</font> : ( (  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b3">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">TT</font></span>)</span> &amp; (  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">T</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">y</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">TT</font> ) ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28_1_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></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="E2:28_1_1"/>
 not  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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"> verum</span><br/>


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