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<div><span class="kw">theorem </span><a NAME="T123"><span class="comment"><font color="firebrick">:: ZF_LANG1:123</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/>  for <font color="Olive" title="b3">M</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">v</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Olive" title="b3">M</font> holds <br/> ( <font color="Olive" title="b3">M</font>,<font color="Olive" title="b4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="zf_lang.html#K9" title="ZF_LANG:func.9">'or'</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b2">q</font></span>)</span></span>)</span> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="zf_lang.html#K9" title="ZF_LANG:func.9">'or'</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b2">q</font></span>)</span></span>)</span> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span></span>)</span> )</div></div>
