<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: MATRIX15:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b6">A</font> being   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of <font color="Olive" title="b4">n</font>,<font color="Olive" title="b3">m</font>,<font color="Olive" title="b5">D</font><br/>  for <font color="Olive" title="b7">B</font> being   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of <font color="Olive" title="b4">n</font>,<font color="Olive" title="b2">k</font>,<font color="Olive" title="b5">D</font><br/>  for <font color="Olive" title="b8">pA</font>, <font color="Olive" title="b9">pB</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b5">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b8">pA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b6">A</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b9">pB</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b7">B</font> holds <br/> <a href="matrix11.html#K3" title="MATRIX11:func.3">ReplaceLine</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Olive" title="b7">B</font></span>)</span>,<font color="Olive" title="b1">i</font>,<span class="p1">(<span class="default"><font color="Olive" title="b8">pA</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b9">pB</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K3" title="MATRIX11:func.3">ReplaceLine</a> (<font color="Olive" title="b6">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b8">pA</font>)</span>)</span> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <span class="p1">(<span class="default"><a href="matrix11.html#K3" title="MATRIX11:func.3">ReplaceLine</a> (<font color="Olive" title="b7">B</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b9">pB</font>)</span>)</span></div></div>
