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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">ThLawOfCosines</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: GTARSKI2:13</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> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <a href="gtarski2.html#K2" title="GTARSKI2:func.2">TarskiEuclid2Space</a> holds  <span class="p1">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>)</span>)</span> <a href="square_1.html#K1" title="SQUARE_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"><span class="p3">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>)</span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">b</font>,<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"><a href="sin_cos.html#K19" title="SIN_COS:func.19">cos</a> <span class="p3">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<span class="p4">(<span class="default"><a href="gtarski2.html#K4" title="GTARSKI2:func.4">Tn2TR</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p4">(<span class="default"><a href="gtarski2.html#K4" title="GTARSKI2:func.4">Tn2TR</a> <font color="Olive" title="b2">b</font></span>)</span>,<span class="p4">(<span class="default"><a href="gtarski2.html#K4" title="GTARSKI2:func.4">Tn2TR</a> <font color="Olive" title="b3">c</font></span>)</span>)</span>)</span></span>)</span></span>)</span></div></div>
