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<b>let </b><font color="Maroon" title="c4">H1</font>, <font color="Maroon" title="c5">H2</font> be    <a href="seqfunc.html#M1" title="SEQFUNC:mode.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green" title="E5">A1</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>  holds  <font color="Maroon" title="c4">H1</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green" title="E6">A2</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>  holds  <font color="Maroon" title="c5">H2</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">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/><a NAME="E1:8_1_2_1"/>
( <font color="Maroon" title="c4">H1</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp; <font color="Maroon" title="c5">H2</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="seqfunc.html#E1:8_1_2"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="seqfunc.html#E2:8_1_2"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E2:8_1_2_1"/>
<font color="Maroon" title="c4">H1</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H2</font> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <font color="Maroon" title="c6">n</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:8_1_2"/>
<font color="Maroon" title="c4">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H2</font>
 <b>by </b><i><a class="ref" href="seqfunc.html#T2" target="_self" title="SEQFUNC:th.2">Th2</a></i>;<br/>


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