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<b>let </b><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">a</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>









<b>assume </b><a NAME="E1:27"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">B</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
<font color="Maroon" title="c5">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"><font color="Olive" title="b1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> : ( <font color="Olive" title="b1">s</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">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Olive" title="b1">s</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b2">t</font> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font><b> such that </b><br/><a NAME="E4:27"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">c</font>
 <b>and </b><br/><a NAME="E5:27"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <b>and </b><br/><a NAME="E6:27"/><i><font color="Green" title="E20">A3</font></i>: 
( <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c6">b</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c7">c</font> )
 ;<br/>
<a NAME="E7:27"/>
<font color="Maroon" title="c6">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="substlat.html#E4:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:27"/><b>then </b>
<font color="Maroon" title="c6">b</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">d</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E10:27"/><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">b</font>
 <b>and </b><br/><a NAME="E11:27"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c8">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="substlat.html#E5:27"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="substlat.html#T10" target="_self" title="SUBSTLAT:th.10">Th10</a></i>;<br/>
<a NAME="E12:27"/><i><font color="Green" title="E23">A6</font></i>: 
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>
 
<b>by </b><i><a class="ref" href="finsub_1.html#D5" title="FINSUB_1:def.5">FINSUB_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">d'</font> = <font color="Maroon" title="c8">d</font>, <font color="Maroon" title="c10">c'</font> = <font color="Maroon" title="c7">c</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="txt" href="substlat.html#E11:27"><i><font color="Green" title="E22">A5</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">d1</font> = <font color="Maroon" title="c8">d</font>, <font color="Maroon" title="c12">b1</font> = <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c13">c1</font> = <font color="Maroon" title="c7">c</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="txt" href="substlat.html#E11:27"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="substlat.html#E12:27"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="partfun1.html#T120" title="PARTFUN1:th.120">PARTFUN1:120</a></i>;<br/>
<a NAME="E15:27"/>
( <font color="Maroon" title="c12">b1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c10">c'</font> &amp; <font color="Maroon" title="c11">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">b1</font> )
 
<b>by </b><i><a class="txt" href="substlat.html#E6:27"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="substlat.html#E10:27"><i><font color="Green" title="E21">A4</font></i></a></i>;<br/>
<a NAME="E16:27"/><b>then </b><i><font color="Green" title="E24">A7</font></i>: 
<font color="Maroon" title="c9">d'</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c10">c'</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#T140" title="PARTFUN1:th.140">PARTFUN1:140</a></i>;<br/>
<a NAME="E17:27"/><b>then </b>
<font color="Maroon" title="c9">d'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c10">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d'</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">c'</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T31" title="FUNCT_4:th.31">FUNCT_4:31</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c14">e</font> = <font color="Maroon" title="c11">d1</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c13">c1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="ref" href="partfun1.html#T119" title="PARTFUN1:th.119">PARTFUN1:119</a></i>;<br/>
<a NAME="E19:27"/>
<font color="Maroon" title="c14">e</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="substlat.html#E4:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="substlat.html#E10:27"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c15">e</font> = <font color="Maroon" title="c14">e</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c15">e</font>
;<br/>

<b>thus </b><a NAME="E21:27"/>
<font color="Maroon" title="c15">e</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="txt" href="substlat.html#E4:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="substlat.html#E10:27"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/>

<b>thus </b><a NAME="E22:27"/>
<font color="Maroon" title="c15">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">B</font>
 <b>by </b><i><a class="txt" href="substlat.html#E6:27"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="substlat.html#E11:27"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="substlat.html#E16:27"><i><font color="Green" title="E24">A7</font></i></a></i>;<br/>


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