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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pzfmisc1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E2:6"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a><br/>

<b>assume </b><a NAME="E3:6"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E4:6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E2:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E5:6"/><b>then </b><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E3:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="pboole.html#D5">PBOOLE:def 5</a></i>;<br/>
<a NAME="E6:6"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="extens_1.html#E1:6"><i><font color="Green">E4</font></i></a>, <a class="txt" href="extens_1.html#E3:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="pzfmisc1.html#D3">PZFMISC1:def 3</a></i>;<br/>
<a NAME="E7:6"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="extens_1.html#E3:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="extens_1.html#E5:6"><i><font color="Green">E7</font></i></a>, <a class="txt" href="extens_1.html#E6:6"><i><font color="Green">E8</font></i></a>, <a class="ref" href="funct_2.html#T9">FUNCT_2:9</a></i>;<br/>


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