<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="circtrm1.html#R2" title="CIRCTRM1:pred.2">are_equivalent</a> <a onclick="hs(this)" href="javascript:()">CIRCTRM1:def 10 : <br/></a><span> 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>  holds <br/> ( <font color="Olive" title="b1">S1</font>,<font color="Olive" title="b2">S2</font> <a href="circtrm1.html#R2" title="CIRCTRM1:pred.2">are_equivalent</a>  iff  ex <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <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> );<br/></span></div>
