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

<span class="kw">let </span><font color="Maroon" title="c1">X</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">  for <font color="Olive" title="b1">l</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Maroon" title="c1">X</font> holds <br/> ( <font color="Olive" title="b1">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Olive" title="b1">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">l</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Olive" title="b1">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">l</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Maroon" title="c1">X</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="c2">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">i1</font> =  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">i2</font> =  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span>;<br/>
<a NAME="E1:41"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c2">l</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  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> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T21" target="_self" onmouseover="rs('coh_sp/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E2:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A2</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <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"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/>
<a NAME="E3:41"/>
(  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T21" target="_self" onmouseover="rs('coh_sp/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E4:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A3</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E5:41"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
 <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font>
 
;<br/>
<a NAME="E6:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A5</font></span>: 
 <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T22" target="_self" onmouseover="rs('coh_sp/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<a NAME="E7:41"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="ref" href="coh_sp.html#T22" target="_self" onmouseover="rs('coh_sp/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:41"/>
<font color="Maroon" title="c2">l</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="txt" href="#E6:41"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="coh_sp.html#E29"><span class="lab"><font color="Green" title="E15">Lm1</font></span></a>, <a class="ref" href="relat_1.html#T52" onmouseover="rs('relat_1/T52')" onmouseout="rh()">RELAT_1:52</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font></span><br/>

<a NAME="E9:41"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
 <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font>
 
;<br/>
<a NAME="E10:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A7</font></span>: 
 <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T22" target="_self" onmouseover="rs('coh_sp/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<a NAME="E11:41"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:41"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="coh_sp.html#T22" target="_self" onmouseover="rs('coh_sp/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:41"/>
<span class="p1">(<span class="default"><a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <span class="p2">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E10:41"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="coh_sp.html#E29"><span class="lab"><font color="Green" title="E15">Lm1</font></span></a>, <a class="ref" href="relat_1.html#T53" onmouseover="rs('relat_1/T53')" onmouseout="rh()">RELAT_1:53</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>
