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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: CIRCTRM1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S1</font>, <font color="Olive" title="b2">S2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">S1</font>,<font color="Olive" title="b2">S2</font> <a href="circtrm1.html#R1" title="CIRCTRM1:pred.1">are_equivalent_wrt</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g</font> holds <br/>(  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">S2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b2">S2</font> )</div></div>
