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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>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#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><a NAME="E1:82"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM2">Point</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#NM2">Point</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>



<b>assume </b><a NAME="E2:82"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:82"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>4</sub></font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E4:82"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:82"><i><font color="Green">E65</font></i></a>, <a class="txt" href="tmap_1.html#E2:82"><i><font color="Green">E66</font></i></a>, <a class="ref" href="tmap_1.html#T81" target="_self">Th81</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:82"><i><font color="Green">E65</font></i></a>, <a class="ref" href="tmap_1.html#T78" target="_self">Th78</a></i>;<br/>


</div>
