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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: NEWTON06:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">b</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b4">d</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b4">d</font></span>)</span></div></div>
