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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:43_1_2"/><i><font color="Green">E28</font></i>: 
( not <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> is <a href="realset1.html#V1">trivial</a> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> is <a href="realset1.html#V1">trivial</a> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:43_1_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( not <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a> )
 <b>by </b><i><a class="ref" href="pencil_1.html#D20" target="_self">Def20</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="pencil_1.html#E1:43_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="pencil_1.html#E3:43_1_2"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="pencil_1.html#E1:43_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="pencil_1.html#E3:43_1_2"><i><font color="Green">E29</font></i></a></i>
;<br/>


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