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<b>let </b><font color="Maroon">b</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">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:88"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 ;<br/>

<b>let </b><font color="Maroon">d</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:88"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="toprealb.html#K3" target="_self">IntIntervals</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E4:88"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/>
<a NAME="E5:88"/><i><font color="Green">E68</font></i>: 
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="partfun1.html#K2">|</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_2.html#K1">.[</a></span> is <a href="funct_1.html#V2">one-to-one</a>
 
;<br/>
<a NAME="E6:88"/>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:88"/><b>then </b>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_2.html#K1">.[</a></span>
 
<b>by </b><i><a class="ref" href="topreala.html#T20">TOPREALA:20</a></i>;<br/>
<b>hence </b><a NAME="E8:88"/>
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="partfun1.html#K2">|</a> <font color="Maroon">d</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i>, , <a class="ref" href="sin_cos6.html#T2">SIN_COS6:2</a></i>;<br/>


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