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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <font color="Maroon" title="c1">n</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">M</font> being   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> holds  <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Olive" title="b2">f2</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="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be  <font color="Maroon" title="c1">n</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> holds  <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</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="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">M</font> be   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</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="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f2</font></span>)</span></span><br/>









<font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font> = 
<font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T31" title="RVSUM_1:th.31">RVSUM_1:31</a></span>
<br/>.= 
<font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T54" title="RVSUM_1:th.54">RVSUM_1:54</a></span>
;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T22" target="_self" title="MATRTOP1:th.22">Th22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T23" target="_self" title="MATRTOP1:th.23">Th23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T54" title="RVSUM_1:th.54">RVSUM_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T31" title="RVSUM_1:th.31">RVSUM_1:31</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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