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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th72</font></span>: <a NAME="T67"><span class="comment"><font color="firebrick">:: GROUP_22:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b4">f1</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/>  for <font color="Olive" title="b5">f2</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font><br/>  for <font color="Olive" title="b6">A</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G1</font> holds   <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b6">A</font></span>)</span></span>)</span>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b6">A</font></span>)</span></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f1</font></span>)</span> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b6">A</font></span>)</span>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f1</font></span>)</span> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b6">A</font></span>)</span> #)</div></div>
