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<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>) <b>-&gt; </b>  <a href="relset_1.html#M2">M5</a>(<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>) = the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E2:57_1_1"/><i><font color="Green">E33</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) )
 <b>from </b><i><a class="ref" href="prvect_1.html#S1" target="_self">PRVECT_1:sch 1</a>();<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><a NAME="E1:57_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="prvect_1.html#D12" target="_self">Def12</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:57_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:57_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="prvect_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E4:57_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> is   <a href="binop_1.html#NM2">BinOp</a> of <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="prvect_1.html#M1" target="_self">BinOps</a> of  <a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="prvect_1.html#E2:57_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="prvect_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E5:57_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:57_1_1"><i><font color="Green">E33</font></i></a></i>;<br/>


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