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<b>let </b><font color="Maroon" title="c1">E</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <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="Maroon" title="c1">E</font>;<br/><b>let </b><font color="Maroon" title="c3">H</font>, <font color="Maroon" title="c4">H'</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>







<a NAME="E1:32"/>
( ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font></span>)</span> implies ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font> &amp; <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font> ) ) &amp; ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font> &amp; <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font></span>)</span> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font></span>)</span> ) &amp; ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font> &amp; <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> ) &amp; ( ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> ) implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H'</font> ) &amp; ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> ) &amp; ( ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> ) implies <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H</font> ) )
 
<b>by </b><i><a class="ref" href="zf_model.html#T15" target="_self" title="ZF_MODEL:th.15">Th15</a>, <a class="ref" href="zf_model.html#T18" target="_self" title="ZF_MODEL:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E2:32"/>
( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c4">H'</font> iff ( <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> iff <font color="Maroon" title="c1">E</font>,<font color="Maroon" title="c2">f</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H'</font> ) )
 ;<br/>


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