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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">D'</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c3">S</font> be   <a href="finseq_2.html#NM2" title="FINSEQ_2:NM.2">FinSequence-DOMAIN</a> of <font color="Maroon" title="c2">D'</font>;<br/>





<a NAME="E1:107"/>
<font color="Maroon" title="c3">S</font> is    <a href="finseq_2.html#M1" title="FINSEQ_2:mode.1">FinSequenceSet</a> of <font color="Maroon" title="c1">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="finseq_2.html#D3" target="_self" title="FINSEQ_2:def.3">FINSEQ_2:def 3</a><br/>

<b>assume </b><a NAME="E1:107_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">a</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">D'</font> <b>by </b><i><a class="ref" href="finseq_2.html#D3" target="_self" title="FINSEQ_2:def.3">Def3</a></i>;<br/>
<a NAME="E3:107_1"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D'</font> &amp; <font color="Maroon" title="c2">D'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E4:107_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:107_1"/>
<font color="Maroon" title="c4">a</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:107"/>
<font color="Maroon" title="c3">S</font> is   <a href="finseq_2.html#NM2" title="FINSEQ_2:NM.2">FinSequence-DOMAIN</a> of <font color="Maroon" title="c1">D</font>
 ;<br/>


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