<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">i</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">  <a href="euclid.html#K11" title="EUCLID:func.11">sqr</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span><br/>



<a NAME="E1:51"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T147" onmouseover="rs('relat_1/T147')" onmouseout="rh()">RELAT_1:147</a></span>;<br/>
<a NAME="E2:51"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
;<br/>
<a NAME="E3:51"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</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"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="51_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">x</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"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:51_1"/><span class="lab"><font color="Green" title="E31">A4</font></span>: 
<font color="Maroon" title="c3">x</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"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<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="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">nx</font> = <font color="Maroon" title="c3">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/>
<a NAME="E3:51_1"/><span class="lab"><font color="Green" title="E32">A5</font></span>: 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51_1"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E4:51_1"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51_1"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E5:51_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A7</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">nx</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/>
<a NAME="E6:51_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixr2.html#T74" onmouseover="rs('matrixr2/T74')" onmouseout="rh()">MATRIXR2:74</a></span>;<br/>
<a NAME="E7:51_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A8</font></span>: 
<font color="Maroon" title="c4">nx</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:51_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:51_1_1"/>
( <font color="Maroon" title="c4">nx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> or <font color="Maroon" title="c4">nx</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">i</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:51_1_1_1"/><span class="lab"><font color="Green" title="E36">A9</font></span>: 
<font color="Maroon" title="c4">nx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</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"> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> = 
<a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E7:51_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E3:51_1"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="matrixr2.html#T75" onmouseover="rs('matrixr2/T75')" onmouseout="rh()">MATRIXR2:75</a></span>
<br/>.= 
1 <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D2" onmouseover="rs('rvsum_1/D2')" onmouseout="rh()">RVSUM_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E7:51_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E1:51_1_1_1"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="matrixr2.html#T75" onmouseover="rs('matrixr2/T75')" onmouseout="rh()">MATRIXR2:75</a></span>
;<br/> <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:51_1_1_2"/><span class="lab"><font color="Green" title="E36">A10</font></span>: 
<font color="Maroon" title="c4">nx</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">i</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"> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> = 
<a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E7:51_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E3:51_1"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="matrixr2.html#T76" onmouseover="rs('matrixr2/T76')" onmouseout="rh()">MATRIXR2:76</a></span>
<br/>.= 
<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D2" onmouseover="rs('rvsum_1/D2')" onmouseout="rh()">RVSUM_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E7:51_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E1:51_1_1_2"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="ref" href="matrixr2.html#T76" onmouseover="rs('matrixr2/T76')" onmouseout="rh()">MATRIXR2:76</a></span>
;<br/> <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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="euclid_7.html#T2" target="_self" onmouseover="rs('euclid_7/T2')" onmouseout="rh()">Th1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:51"/>
 <a href="euclid.html#K11" title="EUCLID:func.11">sqr</a> <span class="p1">(<span class="default"><a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_7.html#K6" title="EUCLID_7:func.6">Base_FinSeq</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="funct_1.html#T2" onmouseover="rs('funct_1/T2')" onmouseout="rh()">FUNCT_1:2</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/>


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