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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Threcursive0101</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: POSET_2:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</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="b3">D</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">I</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b5">J</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>,<font color="Olive" title="b2">Y</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b6">E1</font>, <font color="Olive" title="b7">E2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b8">W</font> being   <a href="poset_1.html#V2" title="POSET_1:attr.2">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="poset_2.html#K7" title="POSET_2:func.7">FlatConF</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="poset_2.html#K7" title="POSET_2:func.7">FlatConF</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>,<span class="p1">(<span class="default"><a href="poset_2.html#K7" title="POSET_2:func.7">FlatConF</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span> st <br/> for <font color="Olive" title="b9">f</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b9">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> (<span class="p3">(<span class="default"><a href="poset_2.html#K4" title="POSET_2:func.4">FlatPoset</a> <font color="Olive" title="b1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="poset_2.html#K4" title="POSET_2:func.4">FlatPoset</a> <font color="Olive" title="b2">Y</font></span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> (<span class="p3">(<span class="default"><a href="poset_2.html#K4" title="POSET_2:func.4">FlatPoset</a> <font color="Olive" title="b1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="poset_2.html#K4" title="POSET_2:func.4">FlatPoset</a> <font color="Olive" title="b2">Y</font></span>)</span>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/><font color="Olive" title="b8">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="poset_2.html#K11" title="POSET_2:func.11">RecFunc02</a> (<span class="p1">(<span class="default"><font color="Olive" title="b9">f</font> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b9">f</font> <a href="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a></span>)</span>,<font color="Olive" title="b6">E1</font>,<font color="Olive" title="b7">E2</font>,<font color="Olive" title="b4">I</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b3">D</font>)</div></div>
