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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="relset_1.html#M2" title="RELSET_1:mode.2">M5</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#K17" title="PRVECT_1:func.17">.</a> $1</span>)</span>,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="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</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="E2:57_2_1"/><i><font color="Green" title="E33">A5</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">i</font> be    <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/><a NAME="E1:57_2_1_1"/>
 <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>
 <b>by </b><i><a class="ref" href="prvect_1.html#D12" target="_self" title="PRVECT_1:def.12">Def12</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">j</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> <font color="Maroon" title="c1">g</font> <b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:57_2_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#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</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="c3">i</font></span>)</span> &amp; 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="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c4">j</font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:57_2_1"><i><font color="Green" title="E33">A5</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="E4:57_2_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> is   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <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">p'</font> = <font color="Maroon" title="c2">p</font> as    <a href="prvect_1.html#M2" title="PRVECT_1:mode.2">UnOps</a> of  <a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font> <b>by </b><i><a class="txt" href="prvect_1.html#E2:57_2_1"><i><font color="Green" title="E33">A5</font></i></a>, <a class="ref" href="prvect_1.html#T20" target="_self" title="PRVECT_1:th.20">Th20</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">p'</font>
;<br/>

<b>thus </b><a NAME="E5:57_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">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="c3">p'</font> <a href="prvect_1.html#K11" title="PRVECT_1:func.11">.</a> <font color="Olive" title="b1">i</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</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#E2:57_2_1"><i><font color="Green" title="E33">A5</font></i></a></i>;<br/>


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