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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">P4</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: REALALG2:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b3">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span></div></div>
