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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being 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>   st <font color="Olive" title="b1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Olive" title="b1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> holds <br/><font color="Olive" title="b1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c2">q</font></span><br/><b>let </b><font color="Maroon" title="c3">M</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> implies <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c2">q</font> )</span><br/>





<b>assume </b><a NAME="E1:113"/><i><font color="Green" title="E36">A1</font></i>: 
( <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">p</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c2">q</font></span><br/>

<b>let </b><font color="Maroon" title="c4">v</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="c3">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D5" title="ZF_MODEL:def.5">ZF_MODEL:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">q</font></span><br/>

<a NAME="E2:113"/>
( <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">p</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="txt" href="#E1:113"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="zf_model.html#D5" title="ZF_MODEL:def.5">ZF_MODEL:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:113"/>
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="ref" href="zf_model.html#T18" title="ZF_MODEL:th.18">ZF_MODEL:18</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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