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<span class="kw">let </span><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">nt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b5">mt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b5">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b3">B</font></span>)</span>,<font color="Olive" title="b4">nt</font>,<font color="Olive" title="b5">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">nt</font>,<font color="Olive" title="b5">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Olive" title="b3">B</font>,<font color="Olive" title="b4">nt</font>,<font color="Olive" title="b5">mt</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c3">K</font><br/>  for <font color="Olive" title="b3">nt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b4">mt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Olive" title="b1">A</font> holds <br/> <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b2">B</font></span>)</span>,<font color="Olive" title="b3">nt</font>,<font color="Olive" title="b4">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">nt</font>,<font color="Olive" title="b4">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">nt</font>,<font color="Olive" title="b4">mt</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c3">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">nt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b2">mt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c4">A</font> holds <br/> <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">mt</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">nt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">mt</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c4">A</font> holds <br/> <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Olive" title="b1">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Olive" title="b1">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Olive" title="b1">mt</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">mt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c7">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c4">A</font> implies  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> )</span><br/>











<span class="kw">assume </span><a NAME="E1:1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">nt</font></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c7">mt</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>)</span></a><div class="add"><a NAME="E1:1_1"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
 <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T26" onmouseover="rs('matrix_0/T26')" onmouseout="rh()">MATRIX_0:26</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c8">i</font>, <font color="Maroon" title="c9">j</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>) )</span><br/><span class="kw">assume </span><a NAME="E2:1_1"/><span class="lab"><font color="Green" title="E4">A3</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>)</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c10">nti</font> = <font color="Maroon" title="c6">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">i</font>, <font color="Maroon" title="c11">mtj</font> = <font color="Maroon" title="c7">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#T12" onmouseover="rs('valued_0/T12')" onmouseout="rh()">VALUED_0:12</a></span>;<br/><a NAME="E4:1_1"/><span class="lab"><font color="Green" title="E5">A4</font></span>: 
 <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T26" onmouseover="rs('matrix_0/T26')" onmouseout="rh()">MATRIX_0:26</a></span>;<br/><a NAME="E5:1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A5</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c4">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E2:1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="matrix13.html#T17" onmouseover="rs('matrix13/T17')" onmouseout="rh()">MATRIX13:17</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c10">nti</font>,<font color="Maroon" title="c11">mtj</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="matrix13.html#D1" onmouseover="rs('matrix13/D1')" onmouseout="rh()">MATRIX13:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c10">nti</font>,<font color="Maroon" title="c11">mtj</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c10">nti</font>,<font color="Maroon" title="c11">mtj</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:1_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="matrix_3.html#D3" onmouseover="rs('matrix_3/D3')" onmouseout="rh()">MATRIX_3:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c10">nti</font>,<font color="Maroon" title="c11">mtj</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E4:1_1"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="matrix13.html#D1" onmouseover="rs('matrix13/D1')" onmouseout="rh()">MATRIX13:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E4:1_1"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E1:1_1"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="matrix13.html#D1" onmouseover="rs('matrix13/D1')" onmouseout="rh()">MATRIX13:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">j</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E4:1_1"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="matrix_3.html#D3" onmouseover="rs('matrix_3/D3')" onmouseout="rh()">MATRIX_3:def 3</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:1"/>
 <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> (<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">nt</font>,<font color="Maroon" title="c7">mt</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T27" onmouseover="rs('matrix_0/T27')" onmouseout="rh()">MATRIX_0:27</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
