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<div><span class="kw">theorem </span><a NAME="T143"><span class="comment"><font color="firebrick">:: ABCMIZ_1:143</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="abcmiz_1.html#V3" title="ABCMIZ_1:attr.3">initialized</a>  <a href="abcmiz_1.html#NM5" title="ABCMIZ_1:NM.5">ConstructorSignature</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="abcmiz_1.html#V15" title="ABCMIZ_1:attr.15">irrelevant</a>  <a href="abcmiz_1.html#NM13" title="ABCMIZ_1:NM.13">valuation</a> of <font color="Olive" title="b1">C</font>  st (  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being   <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">f</font> &amp; <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <font color="Olive" title="b1">C</font> holds <br/>( <font color="Olive" title="b5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">g</font> &amp; <font color="Olive" title="b3">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <font color="Olive" title="b1">C</font> ) ) holds <br/> for <font color="Olive" title="b4">e</font> being   <a href="abcmiz_1.html#NM6" title="ABCMIZ_1:NM.6">expression</a> of <font color="Olive" title="b1">C</font>  st  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b4">e</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">f</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b4">e</font> <a href="abcmiz_1.html#K56" title="ABCMIZ_1:func.56">at</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="abcmiz_1.html#K56" title="ABCMIZ_1:func.56">at</a> <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e</font></div></div>
