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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">M1</font>, <font color="Olive" title="b3">M2</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b2">M1</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  &amp; <font color="Olive" title="b3">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  holds <br/><font color="Olive" title="b2">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Olive" title="b3">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">M1</font>, <font color="Olive" title="b2">M2</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">M1</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  &amp; <font color="Olive" title="b2">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  holds <br/><font color="Olive" title="b1">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Olive" title="b2">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">M1</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  &amp; <font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  implies <font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:38"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c3">M1</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> 
 <span class="kw">and </span><br/><a NAME="E2:38"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> </span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_6.html#K1" title="MATRIX_6:func.1">-</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#T24" target="_self" title="MATRIX_6:th.24">Th24</a></span>
<br/>.= 
<font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_6.html#K1" title="MATRIX_6:func.1">-</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="matrix_6.html#D5" target="_self" title="MATRIX_6:def.5">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <span class="p1">(<span class="default"><a href="matrix_6.html#K1" title="MATRIX_6:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#T27" target="_self" title="MATRIX_6:th.27">Th27</a></span>
<br/>.= 
<font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Maroon" title="c4">M2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="matrix_6.html#D5" target="_self" title="MATRIX_6:def.5">Def5</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:38"/>
<font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K3" title="MATRIX_6:func.3">-</a> <font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V2" title="MATRIX_6:attr.2">symmetric</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#D5" target="_self" title="MATRIX_6:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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