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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">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>assume </b><a NAME="E1:22_1_1_1"/><i><font color="Green" title="E9">A</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c3">p</font></span>)</span>
 ;<br/><a NAME="E2:22_1_1_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="txt" href="rewrite2.html#E1:22_1_1_1"><i><font color="Green" title="E9">A</font></i></a>, <a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">defConcatL</a></i>;<br/><a NAME="E3:22_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <font color="Maroon" title="c4">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">defConcatL</a></i>;<br/><b>hence </b><a NAME="E4:22_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> 
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:22_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c3">p</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#T14" title="FINSEQ_2:th.14">FINSEQ_2:14</a></i>;<br/>


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