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<div>:: <span class="kw">deftheorem </span>   defines <a href="comput_1.html#K12" title="COMPUT_1:func.12">composition-closure</a> <a onclick="hs(this)" href="javascript:()">COMPUT_1:def 19 : <br/></a><span> for <font color="Olive" title="b1">Q</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span> holds   <a href="comput_1.html#K12" title="COMPUT_1:func.12">composition-closure</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3"><a href="funct_6.html#K5" title="FUNCT_6:func.5">&lt;:</a><span class="default"><font color="Olive" title="b3">F</font></span><a href="funct_6.html#K5" title="FUNCT_6:func.5">:&gt;</a></span></span>)</span> where <font color="Olive" title="b2">f</font> is    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>, <font color="Olive" title="b3">F</font> is   <a href="comput_1.html#V3" title="COMPUT_1:attr.3">with_the_same_arity</a>   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  : ( <font color="Olive" title="b2">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Q</font> &amp;  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">F</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Q</font> ) </span> } </span> ;<br/></span></div>
