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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: GROUP_17:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st (  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font>  ex <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b5">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b6">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b6">b</font> ) ) &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/> ex <font color="Olive" title="b4">h</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span>,<font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b5">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b6">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">B</font> holds <br/><font color="Olive" title="b4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="group_7.html#K5" title="GROUP_7:func.5">&lt;*</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font></span><a href="group_7.html#K5" title="GROUP_7:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b6">b</font> ) )</div></div>
