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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">y1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <br/>  for <font color="Olive" title="b4">x2</font>, <font color="Olive" title="b5">y2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x2</font> &amp; <font color="Olive" title="b3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">y2</font> &amp; (  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b6">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> <font color="Olive" title="b2">x1</font> holds <br/><font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b6">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b6">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b5">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span>) ) holds <br/><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">y2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <br/>  for <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">y2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x2</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">y2</font> &amp; (  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b5">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> <font color="Olive" title="b1">x1</font> holds <br/><font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b5">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b5">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span>) ) holds <br/><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">y2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">y1</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x2</font>, <font color="Olive" title="b2">y2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x2</font> &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">y2</font> &amp; (  for <font color="Olive" title="b3">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b3">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> <font color="Maroon" title="c3">x1</font> holds <br/><font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b3">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b3">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">i</font></span>)</span>) ) holds <br/><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b1">x2</font>,<font color="Olive" title="b2">y2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">y2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">y2</font> &amp; (  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">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> <font color="Maroon" title="c3">x1</font> holds <br/><font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>) ) implies <font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font>
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font>
 <span class="kw">and </span><br/><a NAME="E3:45"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">y2</font>
 <span class="kw">and </span><br/><a NAME="E4:45"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
 for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">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> <font color="Maroon" title="c3">x1</font> holds <br/><font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span><br/>

<a NAME="E5:45"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E39">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">i</font> &amp; <font color="Maroon" title="c7">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">i</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45_1"/><span class="lab"><font color="Green" title="E40">A7</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">and </span><br/><a NAME="E2:45_1"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span><br/><a NAME="E3:45_1"/><span class="lab"><font color="Green" title="E42">A9</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E2:45_1"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/><a NAME="E4:45_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A10</font></span>: 
<font color="Maroon" title="c7">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> <font color="Maroon" title="c3">x1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><a NAME="E5:45_1"/><span class="lab"><font color="Green" title="E44">A11</font></span>: 
<font color="Maroon" title="c7">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">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E1:45_1"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E3:45_1"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><a NAME="E6:45_1"/>
<font color="Maroon" title="c7">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="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E2:45_1"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> = 
<font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">y1</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T22" title="FUNCOP_1:th.22">FUNCOP_1:22</a></span>
<br/>.= 
<font color="Maroon" title="c2">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">y2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="txt" href="#E4:45_1"><span class="lab"><font color="Green" title="E43">A10</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45_1"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="funcop_1.html#T22" title="FUNCOP_1:th.22">FUNCOP_1:22</a></span>
;<br/> <a class="txt" 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>
<a NAME="E7:45"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="finseq_2.html#T72" title="FINSEQ_2:th.72">FINSEQ_2:72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:45"/>
<font color="Maroon" title="c1">C</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E6:45"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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