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<b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">H'</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>







<a NAME="E1:31"/>
( ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span></span>)</span> implies  not <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span> ) &amp; ( not <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span> implies <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span> implies ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> &amp; <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font> ) ) &amp; ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> &amp; <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font> implies <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K7">'&amp;'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font></span>)</span> ) &amp; ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font> implies  not <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H'</font> ) &amp; ( not <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H'</font> implies <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H'</font> ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:31"/>
( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">H'</font> iff ( <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font> implies <font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H'</font> ) )
 ;<br/>


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