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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">n</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/><i><font color="Green" title="E27">A1</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <font color="Maroon" title="c2">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T15" title="SEQ_1:th.15">SEQ_1:15</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T20" title="SEQ_1:th.20">SEQ_1:20</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p3">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p3">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T11" title="SEQ_1:th.11">SEQ_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T11" title="SEQ_1:th.11">SEQ_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T14" title="SEQ_1:th.14">SEQ_1:14</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font>

;<br/><b>hence </b><a NAME="E3:26_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">n</font>
 <b>by </b><i><a class="txt" href="lp_space.html#E1:26_1"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:26"/>
<font color="Maroon" title="c1">a</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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