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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th50</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: BCIALG_6:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">X9</font> being   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a><br/>  for <font color="Olive" title="b3">I</font> being    <a href="bcialg_1.html#M2" title="BCIALG_1:mode.2">Ideal</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">RI</font> being    <a href="bcialg_2.html#M5" title="BCIALG_2:mode.5">I-congruence</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b3">I</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="bcialg_6.html#NM1" title="BCIALG_6:NM.1">BCI-homomorphism</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">X9</font>  st <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_6.html#K4" title="BCIALG_6:func.4">Ker</a> <font color="Olive" title="b5">f</font> holds <br/> ex <font color="Olive" title="b6">h</font> being   <a href="bcialg_6.html#NM1" title="BCIALG_6:NM.1">BCI-homomorphism</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="bcialg_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Olive" title="b4">RI</font></span>)</span>,<font color="Olive" title="b2">X9</font> st <br/>( <font color="Olive" title="b5">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="bcialg_6.html#K5" title="BCIALG_6:func.5">nat_hom</a> <font color="Olive" title="b4">RI</font></span>)</span> &amp; <font color="Olive" title="b6">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )</div></div>
