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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: ALGSPEC1:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font> &amp; <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Olive" title="b1">S</font> holds <br/><span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b3">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Olive" title="b1">S</font>,<font color="Olive" title="b1">S</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>)</div></div>
