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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">M</font> being  <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">D</font> holds  <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> is   <a href="matrixj1.html#NM3" title="MATRIXJ1:NM.3">FinSequence_of_Square-Matrix</a> of <font color="Olive" title="b1">D</font></span><br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being  <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">D</font> holds  <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> is   <a href="matrixj1.html#NM3" title="MATRIXJ1:NM.3">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c2">D</font></span><br/><b>let </b><font color="Maroon" title="c3">M</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> is   <a href="matrixj1.html#NM3" title="MATRIXJ1:NM.3">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c2">D</font></span><br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>now </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>; <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"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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="Olive" title="b1">n</font>,<font color="Maroon" title="c2">D</font> )</span><br/><b>assume </b><a NAME="E1:71_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"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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="Olive" title="b1">n</font>,<font color="Maroon" title="c2">D</font></span><br/><b>take </b><font color="Maroon" title="c5">n</font> = <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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">n</font>,<font color="Maroon" title="c2">D</font></span><br/><a NAME="E2:71_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default">1</span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E3:71_1"/><b>then </b>
( <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="txt" href="matrixj1.html#E1:71_1"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:71_1"/>
<span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></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">n</font>,<font color="Maroon" title="c2">D</font>
 ; <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="E2:71"/>
<span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> is   <a href="matrixj1.html#NM3" title="MATRIXJ1:NM.3">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c2">D</font>
 <b>by </b><i><a class="ref" href="matrixj1.html#D6" target="_self" title="MATRIXJ1:def.6">Def6</a></i>; <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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