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<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> $1</span>)</span> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> $1</span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c2">p</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E2:54_3_1"/><i><font color="Green" title="E33">A9</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> holds  <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">i</font>) ) )
 <b>from </b><i><a class="ref" href="prvect_1.html#S1" target="_self" title="PRVECT_1:sch.1">PRVECT_1:sch 1</a>();<br/></i>
<a NAME="E3:54_3_1"/><i><font color="Green" title="E34">A10</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">g</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="prvect_1.html#D12" target="_self" title="PRVECT_1:def.12">Def12</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_3_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:54_3_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">i</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon" title="c5">x'</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">g</font> <b>by </b><i><a class="txt" href="prvect_1.html#E3:54_3_1"><i><font color="Green" title="E34">A10</font></i></a></i>;<br/><a NAME="E4:54_3_1_1"/>
( <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> <font color="Maroon" title="c4">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K15" title="PRVECT_1:func.15">.</a> <font color="Maroon" title="c5">x'</font></span>)</span> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:54_3_1"><i><font color="Green" title="E33">A9</font></i></a>, <a class="ref" href="prvect_1.html#D12" target="_self" title="PRVECT_1:def.12">Def12</a></i>;<br/><b>hence </b><a NAME="E5:54_3_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c3">t</font> = <font color="Maroon" title="c2">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> <b>by </b><i><a class="txt" href="prvect_1.html#E2:54_3_1"><i><font color="Green" title="E33">A9</font></i></a>, <a class="txt" href="prvect_1.html#E3:54_3_1"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">t</font>
;<br/>

<b>thus </b><a NAME="E6:54_3_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> holds  <font color="Maroon" title="c3">t</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:54_3_1"><i><font color="Green" title="E33">A9</font></i></a></i>;<br/>


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