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<span class="kw">let </span><font color="Maroon" title="c1">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">P</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b1">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b2">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b1">K</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">P</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">P</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <font color="Olive" title="b1">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b1">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">P</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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"> ( <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> implies  <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>) )</span><br/>





<span class="kw">assume </span><a NAME="E1:2"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</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#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">S</font> =  <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>);<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="2_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="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</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>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</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>)</span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c5">SP</font> =  <a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font>;<br/><span class="kw">let </span><font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c7">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="c6">i</font>,<font color="Maroon" title="c7">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="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) )</span><br/><span class="kw">assume </span><a NAME="E1:2_1"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">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="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</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="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>)</span><br/><a NAME="E2:2_1"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 <a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T92" onmouseover="rs('finseq_3/T92')" onmouseout="rh()">FINSEQ_3:92</a></span>;<br/><a NAME="E3:2_1"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D14" onmouseover="rs('finseq_1/D14')" onmouseout="rh()">FINSEQ_1:def 14</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">Spi</font> = <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c9">Spj</font> = <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">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="E5:2_1"/><span class="lab"><font color="Green" title="E7">A5</font></span>: 
 <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</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#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</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="E6:2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A6</font></span>: 
<span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c8">Spi</font>,<font color="Maroon" title="c9">Spj</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="matrix13.html#D1" onmouseover="rs('matrix13/D1')" onmouseout="rh()">MATRIX13:def 1</a></span>;<br/><a NAME="E7:2_1"/>
(  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font></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> <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="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="matrix_0.html#T24" onmouseover="rs('matrix_0/T24')" onmouseout="rh()">MATRIX_0:24</a>, <a class="ref" href="zfmisc_1.html#T96" onmouseover="rs('zfmisc_1/T96')" onmouseout="rh()">ZFMISC_1:96</a></span>;<br/><a NAME="E8:2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A7</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">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> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E5:2_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="txt" href="#E3:2_1"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="matrix13.html#T17" onmouseover="rs('matrix13/T17')" onmouseout="rh()">MATRIX13:17</a></span>;<br/><a NAME="E9:2_1"/>
(  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <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="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T40" onmouseover="rs('finseq_3/T40')" onmouseout="rh()">FINSEQ_3:40</a>, <a class="ref" href="matrix_0.html#T24" onmouseover="rs('matrix_0/T24')" onmouseout="rh()">MATRIX_0:24</a></span>;<br/><a NAME="E10:2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A8</font></span>: 
( <font color="Maroon" title="c6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> &amp; <font color="Maroon" title="c7">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E5:2_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><a NAME="E11:2_1"/>
( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font> or <font color="Maroon" title="c6">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">j</font> )
 ;<br/><a NAME="E12:2_1"/><span class="kw">then </span>
( ( <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font> &amp; <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font> ) or ( <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font> &amp; <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">Sgm</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E2:2_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E8:2_1"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E10:2_1"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="txt" href="#E6:2_1"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 4</a>, <a class="ref" href="matrix_1.html#D3" onmouseover="rs('matrix_1/D3')" onmouseout="rh()">MATRIX_1:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E13:2_1"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font></span>)</span>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:2_1"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E6:2_1"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="ref" href="matrix_1.html#D3" onmouseover="rs('matrix_1/D3')" onmouseout="rh()">MATRIX_1: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="E3:2"/>
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c3">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</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>
