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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E2">Th2</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: GROUP_14:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a>  ex <font color="Olive" title="b3">I</font> being   <a href="mod_4.html#NM1" title="MOD_4:NM.1">Homomorphism</a> of <span class="p1"><a href="prvect_3.html#K4" title="PRVECT_3:func.4">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="prvect_3.html#K4" title="PRVECT_3:func.4">:]</a></span>,<span class="p1">(<span class="default"><a href="prvect_1.html#K21" title="PRVECT_1:func.21">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="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> st <br/>( <font color="Olive" title="b3">I</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  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">X</font><br/>  for <font color="Olive" title="b5">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">Y</font> holds  <font color="Olive" title="b3">I</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> ) )</div></div>
