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<b>let </b><font color="Maroon">x</font> be   <a href="unialg_1.html#NM1">PFuncFinSequence</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" target="_self">Carrier</a> <font color="Maroon">A</font></span>)</span></span>)</span>, <font color="Maroon">y</font> be   <a href="unialg_1.html#NM1">PFuncFinSequence</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" target="_self">Carrier</a> <font color="Maroon">A</font></span>)</span></span>)</span>;<br/>

<b>assume </b><a NAME="E1:49_1_2"/><i><font color="Green">E38</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K13" target="_self">ComSign</a> <font color="Maroon">A</font></span>)</span> &amp; ( for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> holds <br/><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pralg_1.html#K22" target="_self">[[:</a><span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K23" target="_self">ProdOp</a> <font color="Maroon">A</font>,<font color="Olive">n</font></span>)</span></span><a href="pralg_1.html#K22" target="_self">:]]</a></span> ) &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K13" target="_self">ComSign</a> <font color="Maroon">A</font></span>)</span> &amp; ( for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">y</font> holds <br/><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pralg_1.html#K22" target="_self">[[:</a><span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K23" target="_self">ProdOp</a> <font color="Maroon">A</font>,<font color="Olive">n</font></span>)</span></span><a href="pralg_1.html#K22" target="_self">:]]</a></span> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:49_1_2_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K13" target="_self">ComSign</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:49_1_2_1"/><b>then </b>
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K13" target="_self">ComSign</a> <font color="Maroon">A</font></span>)</span> &amp; <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> &amp; <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:49_1_2_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pralg_1.html#K22" target="_self">[[:</a><span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K23" target="_self">ProdOp</a> <font color="Maroon">A</font>,<font color="Maroon">n</font></span>)</span></span><a href="pralg_1.html#K22" target="_self">:]]</a></span> &amp; <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pralg_1.html#K22" target="_self">[[:</a><span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K23" target="_self">ProdOp</a> <font color="Maroon">A</font>,<font color="Maroon">n</font></span>)</span></span><a href="pralg_1.html#K22" target="_self">:]]</a></span> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:49_1_2_1"/>
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:49_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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