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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> &amp; <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> implies <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> )</span><br/>





<b>assume </b><a NAME="E1:79"/><i><font color="Green" title="E63">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> &amp; <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a></span><br/>

<a NAME="E2:79"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T55" target="_self" title="LUKASI_1:th.55">Th55</a></i>;<br/>
<b>hence </b><a NAME="E3:79"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 <b>by </b><i><a class="txt" href="#E1:79"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="cqc_the1.html#T104" title="CQC_THE1:th.104">CQC_THE1:104</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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