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<b>let </b><font color="Maroon" title="c4">M1</font>, <font color="Maroon" title="c5">M2</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c2">K</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:18_1_2"/><i><font color="Green" title="E6">A22</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font>
 <b>and </b><br/><a NAME="E2:18_1_2"/><i><font color="Green" title="E7">A23</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">M</font> holds <br/><font color="Maroon" title="c4">M1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font></span>)</span>,<font color="Maroon" title="c1">i</font>
 <b>and </b><br/><a NAME="E3:18_1_2"/><i><font color="Green" title="E8">A24</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font>
 <b>and </b><br/><a NAME="E4:18_1_2"/><i><font color="Green" title="E9">A25</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">M</font> holds <br/><font color="Maroon" title="c5">M2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font></span>)</span>,<font color="Maroon" title="c1">i</font>
 ;<br/>

<div><i><font color="Green" title="E10">A26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:18_1_2_1"/><i><font color="Green" title="E11">A27</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">M</font>
 ;<br/><b>hence </b><font color="Maroon" title="c4">M1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> = 
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">k</font></span>)</span>,<font color="Maroon" title="c1">i</font>
<b>by </b><i><a class="txt" href="matrix_2.html#E2:18_1_2"><i><font color="Green" title="E7">A23</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">M2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
<b>by </b><i><a class="txt" href="matrix_2.html#E4:18_1_2"><i><font color="Green" title="E9">A25</font></i></a>, <a class="txt" href="matrix_2.html#E1:18_1_2_1"><i><font color="Green" title="E11">A27</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E6:18_1_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:18_1_2"/>
<font color="Maroon" title="c4">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M2</font>
 <b>by </b><i><a class="txt" href="matrix_2.html#E1:18_1_2"><i><font color="Green" title="E6">A22</font></i></a>, <a class="txt" href="matrix_2.html#E3:18_1_2"><i><font color="Green" title="E8">A24</font></i></a>, <a class="txt" href="matrix_2.html#E5:18_1_2"><i><font color="Green" title="E10">A26</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


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