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

<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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  holds <br/>( <font color="Olive" title="b1">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <font color="Olive" title="b2">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  )</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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-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"> ( <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  implies ( <font color="Maroon" title="c2">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:5"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</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"> ( <font color="Maroon" title="c2">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  )</span><br/>

<a NAME="E2:5"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="cqc_the2.html#E5"><span class="lab"><font color="Green" title="E5">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5"/>
( <font color="Maroon" title="c2">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <font color="Maroon" title="c3">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="cqc_the1.html#T65" onmouseover="rs('cqc_the1/T65')" onmouseout="rh()">CQC_THE1:65</a></span>; <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/>


</div>
