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<b>let </b><font color="Maroon">p</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">M</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">v</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">M</font>;<br/>









<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">M</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:110_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">p</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:110_1_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">q</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font>
 ;<br/><a NAME="E2:110_1_1_1"/><b>then </b>
( ( <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">p</font> or <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">q</font> ) implies <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">r</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T1" target="_self">Th1</a>, <a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/><a NAME="E3:110_1_1_1"/><b>then </b>
( <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font> implies <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">r</font> )
 <b>by </b><i><a class="ref" href="zf_model.html#T17">ZF_MODEL:17</a></i>;<br/><b>hence </b><a NAME="E4:110_1_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:110_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:110_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:110"/>
( <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> &amp; <font color="Maroon">M</font> <a href="zf_model.html#R2">|=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="zf_lang.html#K10">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_model.html#D5">ZF_MODEL:def 5</a></i>;<br/>


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