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<span class="kw">let </span><font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relat_1.html#K1" title="RELAT_1:func.1">K1</a>(<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span>) or  not <font color="Maroon" title="c20">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relat_1.html#K1" title="RELAT_1:func.1">K1</a>(<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span>) or  not <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">y</font> or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c21">g</font> = <a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">f</font> = <a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:87_1_1"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:87_1_1"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c20">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:87_1_1"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/>

<a NAME="E4:87_1_1"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="toprealb.html#E62"><span class="lab"><font color="Green" title="E42">Lm18</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">x</font> = <font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c24">y</font> = <font color="Maroon" title="c20">y</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:87_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>;<br/>
<a NAME="E6:87_1_1"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="toprealb.html#E62"><span class="lab"><font color="Green" title="E42">Lm18</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E7:87_1_1"/><span class="lab"><font color="Green" title="E58">A6</font></span>: 
<font color="Maroon" title="c18">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87_1_1"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E2:87_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<a NAME="E8:87_1_1"/><span class="lab"><font color="Green" title="E59">A7</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87_1_1"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E1:87_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c25">x1</font> =  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font>;<br/>
<a NAME="E9:87_1_1"/><span class="lab"><font color="Green" title="E60">A8</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c23">x</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D6" title="INT_1:def.6">INT_1:def 6</a></span>;<br/>
<a NAME="E10:87_1_1"/><span class="lab"><font color="Green" title="E61">A9</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T69" title="INT_1:th.69">INT_1:69</a></span>;<br/>
<a NAME="E11:87_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T69" title="INT_1:th.69">INT_1:69</a></span>;<br/>
<a NAME="E12:87_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A10</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:87_1_1"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c26">y1</font> =  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font>;<br/>
<a NAME="E13:87_1_1"/><span class="lab"><font color="Green" title="E63">A11</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">y</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c24">y</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D6" title="INT_1:def.6">INT_1:def 6</a></span>;<br/>
<a NAME="E14:87_1_1"/><span class="lab"><font color="Green" title="E64">A12</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T69" title="INT_1:th.69">INT_1:69</a></span>;<br/>
<a NAME="E15:87_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T69" title="INT_1:th.69">INT_1:69</a></span>;<br/>
<a NAME="E16:87_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A13</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:87_1_1"><span class="lab"><font color="Green" title="E64">A12</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<span class="lab"><font color="Green" title="E66">A14</font></span>: <span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font> = 
<a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:87_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">y</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c24">y</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="toprealb.html#T32" target="_self" title="TOPREALB:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_1_1"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E13:87_1_1"><span class="lab"><font color="Green" title="E63">A11</font></span></a>, <a class="txt" href="#E16:87_1_1"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/>
<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Maroon" title="c18">r</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">x</font> = 
<a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c23">x</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="toprealb.html#T32" target="_self" title="TOPREALB:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="toprealb.html#K12" title="TOPREALB:func.12">CircleMap</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_1_1"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E9:87_1_1"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E12:87_1_1"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/>
<a NAME="E19:87_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A15</font></span>: 
 <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_1.html#K4" title="INT_1:func.4">frac</a> <font color="Maroon" title="c24">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_1_1"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E3:87_1_1"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E12:87_1_1"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="txt" href="#E16:87_1_1"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="txt" href="#E17:87_1_1"><span class="lab"><font color="Green" title="E66">A14</font></span></a>, <a class="txt" href="toprealb.html#E75"><span class="lab"><font color="Green" title="E52">Lm23</font></span></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></span>;<br/>
<a NAME="E20:87_1_1"/><span class="lab"><font color="Green" title="E68">A16</font></span>: 
<font color="Maroon" title="c24">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c18">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87_1_1"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E2:87_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<a NAME="E21:87_1_1"/>
<font color="Maroon" title="c18">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87_1_1"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E1:87_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="xxreal_1.html#T3" title="XXREAL_1:th.3">XXREAL_1:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:87_1_1"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:87_1_1"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E7:87_1_1"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E20:87_1_1"><span class="lab"><font color="Green" title="E68">A16</font></span></a>, <a class="txt" href="#E19:87_1_1"><span class="lab"><font color="Green" title="E67">A15</font></span></a>, <a class="ref" href="topreala.html#T7" title="TOPREALA:th.7">TOPREALA:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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