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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Maroon" title="c1">A</font> holds   <a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Olive" title="b2">q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Maroon" title="c1">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c3">q</font></span>)</span></span><br/>





<a NAME="E1:68"/>
<font color="Maroon" title="c2">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D4" onmouseover="rs('qc_lang2/D4')" onmouseout="rh()">QC_LANG2:def 4</a></span>;<br/>
<span class="kw">hence </span> <a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T42" target="_self" onmouseover="rs('qc_lang3/T42')" onmouseout="rh()">Th42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T70" target="_self" onmouseover="rs('qc_lang3/T70')" onmouseout="rh()">Th70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T70" target="_self" onmouseover="rs('qc_lang3/T70')" onmouseout="rh()">Th70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <font color="Maroon" title="c3">q</font></span>)</span>

;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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