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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:37"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E2:37"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:37"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green">E17</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E5:37"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="topreala.html#E3:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="topreala.html#E4:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E7:37"/>
<font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="topmetr.html#T10">TOPMETR:10</a></i>;<br/>
<b>hence </b><a NAME="E8:37"/>
<font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="txt" href="topreala.html#E1:37"><i><font color="Green">E15</font></i></a>, <a class="ref" href="topmetr.html#T9">TOPMETR:9</a></i>;<br/>


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