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<div><span class="kw">theorem </span><a NAME="T32"><span class="comment"><font color="firebrick">:: ZF_FUND1:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <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="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b3">v1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>  holds <br/> ( <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <font color="Olive" title="b3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> &amp; <span class="p1">(<span class="default"><a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <font color="Olive" title="b3">v1</font> &amp; <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#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <font color="Olive" title="b3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v1</font> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="zf_fund1.html#E17"><span class="lab"><font color="Green" title="E7">Lm4</font></span></a></span>;<br/></div></div>
