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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="seqfunc.html#M1" target="_self">Functional_Sequence</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K8">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K7">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K8">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K8">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K8">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T26">RFUNCT_1:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K7">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K8">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K7">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K7" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="seqfunc.html#T4" target="_self">Th4</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seqfunc.html#K7" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seqfunc.html#T2" target="_self">Th2</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seqfunc.html#K7" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seqfunc.html#K7" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="seqfunc.html#E2:20"><i><font color="Green">E14</font></i></a>, <a class="ref" href="seqfunc.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="seqfunc.html#K8" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seqfunc.html#T6" target="_self">Th6</a></i>
;<br/>


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