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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:71"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E2:71"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font> be  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> =  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" target="_self">Trectangle</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <b>by </b><i><a class="txt" href="topreala.html#E1:71"><i><font color="Green">E31</font></i></a>, <a class="txt" href="topreala.html#E2:71"><i><font color="Green">E32</font></i></a>, <a class="ref" href="topreala.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E4:71"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> is   <a href="struct_0.html#NM2">Subset</a> of <a href="topalg_2.html#K3">R^1</a>  &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is   <a href="struct_0.html#NM2">Subset</a> of <a href="topalg_2.html#K3">R^1</a>  )
 
<b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E5:71"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> is   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  &amp; <font color="Maroon">c<sub>10</sub></font> is   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  )
 
<b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <a href="topreala.html#K2" target="_self">R2Homeomorphism</a>  <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1">(<span class="default"><a href="topreala.html#K1" target="_self">Trectangle</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <b>by </b><i><a class="txt" href="topreala.html#E1:71"><i><font color="Green">E31</font></i></a>, <a class="txt" href="topreala.html#E2:71"><i><font color="Green">E32</font></i></a>, <a class="ref" href="topreala.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E7:71"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="topreala.html#E1:71"><i><font color="Green">E31</font></i></a>, <a class="txt" href="topreala.html#E2:71"><i><font color="Green">E32</font></i></a>, <a class="ref" href="topreala.html#T58" target="_self">Th58</a></i>;<br/>
<a NAME="E8:71"/><i><font color="Green">E35</font></i>: 
not  <a href="topreala.html#K1" target="_self">Trectangle</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> is <a href="struct_0.html#V3">empty</a>
 
<b>by </b><i><a class="txt" href="topreala.html#E1:71"><i><font color="Green">E31</font></i></a>, <a class="txt" href="topreala.html#E2:71"><i><font color="Green">E32</font></i></a>, <a class="ref" href="topreala.html#T54" target="_self">Th54</a></i>;<br/>
<i><font color="Green">E36</font></i>: <font color="Maroon">c<sub>12</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="borsuk_1.html#K6">:]</a></span> = 
<a href="topreala.html#K2" target="_self">R2Homeomorphism</a>  <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="borsuk_1.html#K6">:]</a></span>
<b>by </b><i><a class="ref" href="extens_1.html#T1">EXTENS_1:1</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="topreala.html#E5:71"><i><font color="Green">E33</font></i></a>, <a class="ref" href="topreala.html#T55" target="_self">Th55</a></i>
;<br/>
<a NAME="E10:71"/>
<span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="borsuk_1.html#K6">:]</a></span> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T46">BORSUK_1:46</a></i>;<br/>
<b>hence </b><a NAME="E11:71"/>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" target="_self">Trectangle</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="topreala.html#E7:71"><i><font color="Green">E34</font></i></a>, <a class="txt" href="topreala.html#E8:71"><i><font color="Green">E35</font></i></a>, <a class="txt" href="topreala.html#E9:71"><i><font color="Green">E36</font></i></a>, <a class="ref" href="topgrp_1.html#T25">TOPGRP_1:25</a></i>;<br/>


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