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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><a NAME="E1:32"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#K4" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang2.html#D12" target="_self">QC_LANG2:def 12</a><br/>

<a NAME="E2:32"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="qc_lang1.html#K18">the_left_argument_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="qc_lang1.html#K19">the_right_argument_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="qc_lang2.html#E1:32"><i><font color="Green">E20</font></i></a>, <a class="ref" href="qc_lang2.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang1.html#V4">conjunctive</a> &amp;  <a href="qc_lang1.html#K18">the_left_argument_of</a> <font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang2.html#V2" target="_self">conditional</a> &amp;  <a href="qc_lang1.html#K19">the_right_argument_of</a> <font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang2.html#V2" target="_self">conditional</a> )
 <b>by </b><i><a class="ref" href="qc_lang2.html#D11" target="_self">Def11</a>, <a class="ref" href="qc_lang1.html#D19">QC_LANG1:def 19</a></i>;<br/>


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