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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">M1</font>, <font color="Olive" title="b3">M2</font>, <font color="Olive" title="b4">M3</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">K</font> holds   <a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Olive" title="b3">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Olive" title="b4">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b2">M1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b3">M2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b4">M3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M1</font>, <font color="Olive" title="b2">M2</font>, <font color="Olive" title="b3">M3</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font> holds   <a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Olive" title="b2">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Olive" title="b3">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b1">M1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b2">M2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Olive" title="b3">M3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font>, <font color="Maroon" title="c5">M3</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c5">M3</font></span>)</span></span><br/>









<a NAME="E1:59"/>
 <a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c5">M3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_8.html#T54" target="_self" title="MATRIX_8:th.54">Th54</a></i>;<br/>
<b>hence </b><a NAME="E2:59"/>
 <a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_8.html#K1" title="MATRIX_8:func.1">Trace</a> <font color="Maroon" title="c5">M3</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrix_8.html#T54" target="_self" title="MATRIX_8:th.54">Th54</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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