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

<b>let </b><font color="Maroon">p1</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> 2</span>)</span>;<br/><b>let </b><font color="Maroon">p2</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> 2</span>)</span>;<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> 2</span>)</span>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">r</font> be  non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>









<b>set </b><font color="Maroon">D</font> =  <a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:105"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">A</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E2:105"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">A</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon">A1</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span> <b>by </b><i><a class="txt" href="jordan.html#E10:105"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jordan.html#E12:105"><i><font color="Green">E80</font></i></a>, <a class="ref" href="topreal1.html#T4">TOPREAL1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A2</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="jordan.html#E10:105"><i><font color="Green">E79</font></i></a>, <a class="ref" href="topreal1.html#T4">TOPREAL1:4</a></i>;<br/>
<b>set </b><font color="Maroon">TA</font> = <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font>;<br/>
<b>consider </b><font color="Maroon">h</font> being   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font></span>)</span><b> such that </b><br/><a NAME="E6:105"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">h</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 <b>and </b><br/><a NAME="E7:105"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <b>and </b><br/><a NAME="E8:105"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="txt" href="jordan.html#E10:105"><i><font color="Green">E79</font></i></a>, <a class="ref" href="topreal1.html#D2">TOPREAL1:def 2</a></i>;<br/>
<a NAME="E9:105"/><i><font color="Green">E78</font></i>: 
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="treal_1.html#T20">TREAL_1:20</a></i>;<br/>
<a NAME="E10:105"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hh</font> = <font color="Maroon">h</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font></span>)</span> <b>by </b><i><a class="ref" href="topmetr.html#T27">TOPMETR:27</a></i>;<br/>
<a NAME="E12:105"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A1</font>
 
<b>by </b><i><a class="ref" href="topalg_5.html#T4">TOPALG_5:4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A1</font></span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span> ;<br/>
<a NAME="E14:105"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E10:105"><i><font color="Green">E79</font></i></a>, <a class="ref" href="jordan6.html#T12">JORDAN6:12</a></i>;<br/>
<a NAME="E15:105"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">A1</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T12">TSEP_1:12</a></i>;<br/>
<a NAME="E16:105"/>
<font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E15:105"><i><font color="Green">E81</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E17:105"/><b>then </b>
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E21:105"><i><font color="Green">E83</font></i></a>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>then consider </b><font color="Maroon">g</font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span><b> such that </b><br/><a NAME="E19:105"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="jordan.html#T10" target="_self">Th10</a>, <a class="txt" href="jordan.html#E13"><i><font color="Green">Lemma84</font></i></a>, <a class="ref" href="tietze.html#T25">TIETZE:25</a></i>;<br/>
<b>reconsider </b><font color="Maroon">R</font> = <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon">R</font>
;<br/>

<a NAME="E21:105"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">hh</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E15:105"><i><font color="Green">E81</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E22:105"/>
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E19:105"><i><font color="Green">E82</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E23:105"/><b>then </b>
<font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>hence </b><a NAME="E24:105"/>
<font color="Maroon">R</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>

<a NAME="E25:105"/><i><font color="Green">E109</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E26:105"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E27:105"/><b>then </b><i><font color="Green">E110</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="txt" href="jordan.html#E12:105"><i><font color="Green">E80</font></i></a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E28:105"/><i><font color="Green">E115</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:105_1"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font></span>)</span>
 ;<br/><a NAME="E2:105_1"/><i><font color="Green">E118</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">p</font>,<font color="Maroon">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E3:105_1"/><i><font color="Green">E119</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:105_1"/><i><font color="Green">E120</font></i>: 
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="txt" href="jordan.html#E19:105"><i><font color="Green">E82</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/><a NAME="E5:105_1"/><i><font color="Green">E121</font></i>: 
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span> is <a href="funct_2.html#V2">onto</a>
 <b>by </b><i><a class="txt" href="jordan.html#E19:105"><i><font color="Green">E82</font></i></a>, </i>;<br/><a NAME="E6:105_1"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">hh</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">hh</font> is <a href="funct_2.html#V2">onto</a> )
 <b>by </b><i><a class="txt" href="jordan.html#E15:105"><i><font color="Green">E81</font></i></a>, , <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/><i><font color="Green">E123</font></i>: <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p5">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p5">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="topgrp_1.html#K4">id</a> <span class="p3">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="grcat_1.html#T56">GRCAT_1:56</a></i>
<br/>.= 
<font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#T12">GRCAT_1:12</a></i>
<br/>.= 
 <a href="topgrp_1.html#K4">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="grcat_1.html#T56">GRCAT_1:56</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">R</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="jordan.html#E16"><i><font color="Green">Lemma89</font></i></a>, <a class="ref" href="jordan.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="jordan.html#T13" target="_self">Th13</a>, <a class="ref" href="jordan.html#T14" target="_self">Th14</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p4">(<span class="default"><a href="treal_1.html#K1">(#)</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">hh</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="jordan.html#T13" target="_self">Th13</a>, <a class="txt" href="jordan.html#E16"><i><font color="Green">Lemma89</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="jordan.html#T11" target="_self">Th11</a>, <a class="txt" href="jordan.html#E16"><i><font color="Green">Lemma89</font></i></a>, <a class="ref" href="jordan.html#T13" target="_self">Th13</a>, <a class="txt" href="jordan.html#E21"><i><font color="Green">Lemma93</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E30:105"/>
<font color="Maroon">R</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="txt" href="jordan.html#E16"><i><font color="Green">Lemma89</font></i></a>, <a class="ref" href="jordan.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
