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<b>let </b><font color="Maroon" title="c1">H1</font>, <font color="Maroon" title="c2">H2</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>let </b><font color="Maroon" title="c4">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> ;<br/>







<b>assume </b><a NAME="E1:123"/><i><font color="Green" title="E39">A1</font></i>: 
( not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H1</font> &amp; ( for <font color="Olive" title="b1">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="Maroon" title="c4">M</font> holds  <font color="Maroon" title="c4">M</font>,<font color="Olive" title="b1">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">H2</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><br/>

<b>let </b><font color="Maroon" title="c5">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="c4">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><br/>

<a NAME="E2:123"/>
( ( for <font color="Olive" title="b1">m</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">M</font> holds  <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">m</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">H2</font> ) &amp; <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:123"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="zf_lang1.html#T140" target="_self" title="ZF_LANG1:th.140">Th140</a></i>;<br/>
<a NAME="E3:123"/><b>then </b>
( <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">H2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T80" target="_self" title="ZF_LANG1:th.80">Th80</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="E4:123"/>
<font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">H2</font></span>)</span>
 <b>by </b><i><a class="ref" href="zf_model.html#T18" title="ZF_MODEL:th.18">ZF_MODEL:18</a></i>;<br/>


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