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<a NAME="E1:9_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp; ( for <font color="Olive" title="b1">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds  <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">i</font>,<font color="Olive" title="b1">r</font> ) )
 
<b>by </b><i><a class="ref" href="pdiff_1.html#D5" target="_self" title="PDIFF_1:def.5">Def5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ;<br/><b>then reconsider </b><font color="Maroon" title="c5">r</font> = <font color="Maroon" title="c4">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/><a NAME="E3:9_1_1_1"/><i><font color="Green" title="E7">A2</font></i>: 
<span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c5">r</font>
 <b>by </b><i><a class="ref" href="pdiff_1.html#D5" target="_self" title="PDIFF_1:def.5">Def5</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">IT</font> = <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">r</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/><a NAME="E5:9_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="pdiff_1.html#E3:9_1_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="finseq_7.html#T7" title="FINSEQ_7:th.7">FINSEQ_7:7</a></i>;<br/><a NAME="E6:9_1_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="euclid.html#T2" title="EUCLID:th.2">EUCLID:2</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c7">IT</font> = <font color="Maroon" title="c6">IT</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/><a NAME="E8:9_1_1_1"/>
<font color="Maroon" title="c7">IT</font> is    <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="c1">n</font>
 ;<br/><b>hence </b><a NAME="E9:9_1_1_1"/>
<span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:9_1_1"/>
 <a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">x</font> is   <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> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="pdiff_1.html#E1:9_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a></i>;<br/>


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