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<span class="kw">let </span><font color="Maroon" title="c1">i</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">f</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">g</font> being   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">o1</font>, <font color="Olive" title="b4">o2</font> being    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">g</font>  st <font color="Olive" title="b3">o1</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b4">o2</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Olive" title="b1">f</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b3">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b4">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b3">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b4">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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">g</font> being   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">o1</font>, <font color="Olive" title="b3">o2</font> being    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">g</font>  st <font color="Olive" title="b2">o1</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b3">o2</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b2">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b3">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b2">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b3">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">g</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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">o1</font>, <font color="Olive" title="b2">o2</font> being    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">g</font>  st <font color="Olive" title="b1">o1</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b2">o2</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b1">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b2">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b1">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Olive" title="b2">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">g</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"> ( <font color="Maroon" title="c4">o1</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp; <font color="Maroon" title="c5">o2</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> implies <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:93"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
( <font color="Maroon" title="c4">o1</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp; <font color="Maroon" title="c5">o2</font> is    <a href="flexary1.html#M2" title="FLEXARY1:mode.2">valued_reorganization</a> of <font color="Maroon" title="c2">f</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</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="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/>

<a NAME="E2:93"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="flexary1.html#E64"><span class="lab"><font color="Green" title="E47">Lm7</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E4:93"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> &amp; <font color="Maroon" title="c6">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#T26" onmouseover="rs('rfinseq/T26')" onmouseout="rh()">RFINSEQ:26</a>, <a class="ref" href="classes1.html#T77" onmouseover="rs('classes1/T77')" onmouseout="rh()">CLASSES1:77</a></span>;<br/>
<a NAME="E5:93"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">g1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<a NAME="E7:93"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">g2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<a NAME="E9:93"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="finseq_1.html#T48" onmouseover="rs('finseq_1/T48')" onmouseout="rh()">FINSEQ_1:48</a></span>;<br/>
<a NAME="E10:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A4</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<a NAME="E11:93"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E12:93"/><span class="kw">then </span>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">h</font> = <font color="Maroon" title="c6">h</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">g2</font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">g2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E10:93"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="funct_2.html#T1" onmouseover="rs('funct_2/T1')" onmouseout="rh()">FUNCT_2:1</a></span>;<br/>
<a NAME="E14:93"/>
<font color="Maroon" title="c9">h</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E11:93"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a>, <a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">h</font> = <font color="Maroon" title="c9">h</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">g2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E50">A3</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E53">A6</font></span>: <font color="Maroon" title="c7">g1</font> = 
<font color="Maroon" title="c3">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#T41" target="_self" onmouseover="rs('flexary1/T41')" onmouseout="rh()">Th41</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c10">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="relat_1.html#T36" onmouseover="rs('relat_1/T36')" onmouseout="rh()">RELAT_1:36</a></span>
<br/>.= 
<font color="Maroon" title="c8">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c10">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#T41" target="_self" onmouseover="rs('flexary1/T41')" onmouseout="rh()">Th41</a></span>
;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> = 
 <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D8" target="_self" onmouseover="rs('flexary1/D8')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<a href="binop_2.html#K3" title="BINOP_2:func.3">addcomplex</a> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c7">g1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D11" onmouseover="rs('rvsum_1/D11')" onmouseout="rh()">RVSUM_1:def 11</a></span>
<br/>.= 
<a href="binop_2.html#K3" title="BINOP_2:func.3">addcomplex</a> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c8">g2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:93"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="finsop_1.html#T7" onmouseover="rs('finsop_1/T7')" onmouseout="rh()">FINSOP_1:7</a></span>
<br/>.= 
 <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D11" onmouseover="rs('rvsum_1/D11')" onmouseout="rh()">RVSUM_1:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="flexary1.html#K6" title="FLEXARY1:func.6">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c5">o2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D8" target="_self" onmouseover="rs('flexary1/D8')" onmouseout="rh()">Def8</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>
