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<b>let </b><font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green" title="E5">A4</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> iff  ex <font color="Olive" title="b2">f</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="c2">E</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a> </span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">E</font> ) )
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green" title="E6">A5</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> iff  ex <font color="Olive" title="b2">f</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="c2">E</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a> </span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">E</font> ) )
 ;<br/>

<b>thus </b><a NAME="E3:8_1_2"/>
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">C</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:8_1_2_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 ;<br/>

<a NAME="E2:8_1_2_1"/><b>then </b>
 ex <font color="Olive" title="b1">f</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="c2">E</font> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a> </span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">E</font> )
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:8_1_2"><i><font color="Green" title="E5">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:8_1_2_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E2:8_1_2"><i><font color="Green" title="E6">A5</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:8_1_2"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font>
 ;<br/>

<a NAME="E5:8_1_2"/><b>then </b>
 ex <font color="Olive" title="b1">f</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="c2">E</font> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a> </span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">E</font> )
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E2:8_1_2"><i><font color="Green" title="E6">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:8_1_2"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E1:8_1_2"><i><font color="Green" title="E5">A4</font></i></a></i>;<br/>


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