<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c3">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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="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>let </b><font color="Maroon" title="c5">f</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c3">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> 1</span>)</span>;<br/><b>let </b><font color="Maroon" title="c6">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c3">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c7">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c3">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c8">y</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c3">n</font>;<br/>











<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pdiff_1.html#K3" title="PDIFF_1:func.3">&lt;&gt;*</a> <font color="Maroon" title="c6">g</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c9">h</font> = <span class="p1">(<span class="default"><a href="pdiff_1.html#K1" title="PDIFF_1:func.1">proj</a> 1,1</span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 1 <b>by </b><i><a class="ref" href="pdiff_1.html#T2" target="_self" title="PDIFF_1:th.2">Th2</a></i>;<br/>
<a NAME="E3:26"/>
<span class="p1">(<span class="default"><a href="pdiff_1.html#K6" title="PDIFF_1:func.6">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c8">y</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K1" title="PDIFF_1:func.1">proj</a> 1,1</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pdiff_1.html#K7" title="PDIFF_1:func.7">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c7">x</font>
 
<b>by </b><i><a class="txt" href="pdiff_1.html#E1:26"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="pdiff_1.html#T12" target="_self" title="PDIFF_1:th.12">Th12</a></i>;<br/>
<a NAME="E4:26"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="pdiff_1.html#K6" title="PDIFF_1:func.6">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c8">y</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K1" title="PDIFF_1:func.1">proj</a> 1,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K7" title="PDIFF_1:func.7">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c7">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pdiff_1.html#E1:26"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E5:26"/>
 <a href="pdiff_1.html#K2" title="PDIFF_1:func.2">&lt;&gt;*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="pdiff_1.html#K6" title="PDIFF_1:func.6">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c8">y</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K7" title="PDIFF_1:func.7">reproj</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c7">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>


</div>
