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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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>4</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<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>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>3</sub></font>;<br/>











<b>assume </b><a NAME="E1:58"/><i><font color="Green">E43</font></i>: 
<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/>

<b>assume </b><a NAME="E2:58"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<a NAME="E3:58"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T49" target="_self">Th49</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</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>
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:58"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tmap_1.html#T52" target="_self">Th52</a></i>;<br/>


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