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<a NAME="E1:74_1_1"/>
<font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font> is <a href="matrixj1.html#V2" title="MATRIXJ1:attr.2">Square-Matrix-yielding</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="matrixj1.html#D6" target="_self" title="MATRIXJ1:def.6">MATRIXJ1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">i</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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span> implies  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c1">D</font> )</span><br/>

<b>assume </b><a NAME="E1:74_1_1_1"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c4">i</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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c1">D</font></span><br/>

<b>take </b><font color="Maroon" title="c5">L</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c4">i</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c1">D</font></span><br/>

<b>thus </b><a NAME="E2:74_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c4">i</font> is   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="txt" href="#E1:74_1_1_1"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:74_1_1"/>
<font color="Maroon" title="c2">S</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">n</font> is   <a href="matrixj1.html#NM3" title="MATRIXJ1:NM.3">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c1">D</font>
 ; <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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