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<b>let </b><font color="Maroon">G1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">G2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">G3</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<a NAME="E1:61"/><i><font color="Green">E29</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font>,<font color="Maroon">G3</font></span><a href="finseq_1.html#K11">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font>,<font color="Maroon">G3</font></span><a href="finseq_1.html#K11">*&gt;</a></span> as    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:61"/>
<font color="Maroon">A</font> is <a href="group_7.html#V1" target="_self">HGrStr-yielding</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D1" target="_self">GROUP_7:def 1</a><br/>

<b>assume </b><a NAME="E1:61_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:61_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:61_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3 )
 
<b>by </b><i><a class="txt" href="group_7.html#E1:61"><i><font color="Green">E29</font></i></a>, , <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:61_1"/>
<font color="Maroon">y</font> is  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> 
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:61"/>
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font>,<font color="Maroon">G3</font></span><a href="finseq_1.html#K11">*&gt;</a></span> is   <a href="group_7.html#NM1">HGrStr-Family</a> of <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 ;<br/>


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