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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/>

<b>assume </b><a NAME="E1:24"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang2.html#V3">biconditional</a>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K4">&lt;=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T55">QC_LANG2:55</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E3:24"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="qc_lang3.html#E2:24"><i><font color="Green">E15</font></i></a>, <a class="ref" href="qc_lang2.html#D4">QC_LANG2:def 4</a></i>;<br/>
<b>then </b> <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T14" target="_self">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T20" target="_self">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T20" target="_self">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E5:24"/>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K13">the_left_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K14">the_right_side_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/>


</div>
