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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<b>assume </b><a NAME="E1:6"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">w1</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<b>reconsider </b><font color="Maroon">w3</font> = <font color="Maroon">w1</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  ;<br/>
<b>reconsider </b><font color="Maroon">w</font> = <font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<a NAME="E5:6"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E6:6"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w1</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<i><font color="Green">E55</font></i>:  <a href="jordan2b.html#K1" target="_self">Proj</a> <font color="Maroon">p</font>,<font color="Maroon">i</font> = 
<font color="Maroon">w1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">w3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/>
<a NAME="E8:6"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E9:6"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E10:6"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="euclid.html#K9">*</a> <font color="Maroon">w1</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D11">EUCLID:def 11</a></i>;<br/>
<a NAME="E11:6"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">r</font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
 <a href="jordan2b.html#K1" target="_self">Proj</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">i</font> = 
<font color="Maroon">w</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">w</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan2b.html#K1" target="_self">Proj</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="rvsum_1.html#T67">RVSUM_1:67</a></i>
;<br/>
<b>hence </b><a NAME="E13:6"/>
 <a href="jordan2b.html#K1" target="_self">Proj</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan2b.html#K1" target="_self">Proj</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>
 ;<br/>


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