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<b>let </b><font color="Maroon">X</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">Y</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">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/>









<b>assume </b><a NAME="E1:82"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font>
 ;<br/>

<b>let </b><font color="Maroon">x0</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X0</font>;<br/><b>let </b><font color="Maroon">x1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X1</font>;<br/>



<b>assume </b><a NAME="E2:82"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 ;<br/>

<b>assume </b><a NAME="E3:82"/>
<font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X0</font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">x0</font>
 ;<br/>

<a NAME="E4:82"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X0</font></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X1</font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">x1</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:82"/>
<font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X1</font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">x1</font>
 <b>by </b><i>, </i>;<br/>


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