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<a NAME="E1:35_1_1"/><i><font color="Green">E21</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K1">SubstitutionSet</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="substlat.html#D4">SUBSTLAT:def 4</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="substlat.html#K1">SubstitutionSet</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> =  <a href="substlat.html#K3">mi</a> <span class="p1"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="setwiseo.html#K2">.}</a></span>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>, <a href="substlat.html#K1">SubstitutionSet</a> <font color="Maroon">V</font>,<font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:35_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>
 ;<br/><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> ;<br/><a NAME="E3:35_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K3">mi</a> <span class="p1"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Maroon">a</font></span><a href="setwiseo.html#K2">.}</a></span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:35_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="heyting2.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:35_1_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <b>by </b><i>, <a class="ref" href="funct_2.html#T5">FUNCT_2:5</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E7:35_1_1"/>
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K3">mi</a> <span class="p1"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Olive">a</font></span><a href="setwiseo.html#K2">.}</a></span>
 <b>by </b><i/>;<br/>


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