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<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: MOD_4:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being   <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="mod_4.html#NM1" title="MOD_4:NM.1">Homomorphism</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font><br/>  for <font color="Olive" title="b4">x</font>, <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="b1">G</font> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">H</font> &amp; <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font></span>)</span> &amp; <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">x</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">y</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="mod_4.html#E68"><span class="lab"><font color="Green" title="E32">Lm13</font></span></a>, <a class="txt" href="mod_4.html#E69"><span class="lab"><font color="Green" title="E33">Lm14</font></span></a>, <a class="txt" href="mod_4.html#E70"><span class="lab"><font color="Green" title="E34">Lm15</font></span></a></span>;<br/></div></div>
