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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">R1</font>, <font color="Maroon" title="c3">R</font>, <font color="Maroon" title="c4">R2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:35"/>
<font color="Maroon" title="c2">R1</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <font color="Maroon" title="c3">R</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">R2</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <font color="Maroon" title="c3">R</font>
 ;<br/>

<a NAME="E2:35"/><b>then </b>
<font color="Maroon" title="c2">R1</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c3">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseqop.html#T29" title="FINSEQOP:th.29">FINSEQOP:29</a></i>;<br/>
<a NAME="E3:35"/><b>then </b>
( <font color="Maroon" title="c2">R1</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">R2</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">R</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="finseqop.html#T29" title="FINSEQOP:th.29">FINSEQOP:29</a>, <a class="ref" href="finseqop.html#T77" title="FINSEQOP:th.77">FINSEQOP:77</a>, <a class="ref" href="rvsum_1.html#T22" target="_self" title="RVSUM_1:th.22">Th22</a>, <a class="ref" href="rvsum_1.html#T23" target="_self" title="RVSUM_1:th.23">Th23</a>, <a class="ref" href="binop_2.html#T2" title="BINOP_2:th.2">BINOP_2:2</a></i>;<br/>
<a NAME="E4:35"/><b>then </b>
<font color="Maroon" title="c2">R1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">R2</font> <a href="rvsum_1.html#K5" title="RVSUM_1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> 0</span>)</span>
 
<b>by </b><i><a class="ref" href="binop_2.html#T2" title="BINOP_2:th.2">BINOP_2:2</a>, <a class="ref" href="finseqop.html#T57" title="FINSEQOP:th.57">FINSEQOP:57</a></i>;<br/>
<b>hence </b><a NAME="E5:35"/>
<font color="Maroon" title="c2">R1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">R2</font>
 <b>by </b><i><a class="ref" href="binop_2.html#T2" title="BINOP_2:th.2">BINOP_2:2</a>, <a class="ref" href="finseqop.html#T57" title="FINSEQOP:th.57">FINSEQOP:57</a></i>;<br/>


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