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<b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">g</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>



<b>reconsider </b><font color="Maroon">f1</font> = <font color="Maroon">f</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<b>assume </b><a NAME="E2:7"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> or  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> )
 ;<br/>

<a NAME="E3:7"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g1</font> = <font color="Maroon">g</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E5:7"/>
<font color="Maroon">f1</font> <a href="rvsum_1.html#K4">+</a> <font color="Maroon">g1</font> is    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a> 
 
;<br/>
<b>hence </b><a NAME="E6:7"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>

<b>hence </b><a NAME="E7:7"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>


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