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<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp; <font color="Maroon" title="c2">g</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 &amp; <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:56"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
( <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )
 <span class="kw">and </span><br/><a NAME="E2:56"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
( <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp; <font color="Maroon" title="c2">g</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )
 <span class="kw">and </span><br/><a NAME="E3:56"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
 <span class="kw">and </span><br/><a NAME="E4:56"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j</font> implies  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font> )</span><br/><span class="kw">assume </span><a NAME="E1:56_1"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><a NAME="E2:56_1"/><span class="lab"><font color="Green" title="E41">A6</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E3:56_1"/><span class="lab"><font color="Green" title="E42">A7</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:56_1_1_1"/>
( <font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> or <font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_1"/><span class="lab"><font color="Green" title="E43">A8</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><a NAME="E2:56_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E3:56_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:56_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A9</font></span>: 
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56_1"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="ref" href="topreal8.html#T28" title="TOPREAL8:th.28">TOPREAL8:28</a></span>;<br/><a NAME="E5:56_1_1_1_1"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_1"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="txt" href="#E1:56_1_1_1_1"><span class="lab"><font color="Green" title="E43">A8</font></span></a>, <a class="ref" href="topreal8.html#T28" title="TOPREAL8:th.28">TOPREAL8:28</a></span>;<br/><span class="kw">hence </span><a NAME="E6:56_1_1_1_1"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E4:56_1_1_1_1"><span class="lab"><font color="Green" title="E44">A9</font></span></a>, <a class="ref" href="topreal1.html#D9" title="TOPREAL1:def.9">TOPREAL1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="56_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2"/>
<font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:56_1_1_1_2"/><span class="lab"><font color="Green" title="E43">A10</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><div><span class="lab"><font color="Green" title="E44">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:56_1_1_1_2_1"/>
<font color="Maroon" title="c2">g</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:56_1_1_1_2_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="realset1.html#T13" title="REALSET1:th.13">REALSET1:13</a></span>;<br/><a NAME="E3:56_1_1_1_2_1"/><span class="kw">then </span>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T23" title="NAT_1:th.23">NAT_1:23</a></span>;<br/><a NAME="E4:56_1_1_1_2_1"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#T28" title="TOPREAL1:th.28">TOPREAL1:28</a></span>;<br/><span class="kw">hence </span><a NAME="E5:56_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E39">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">reconsider </span><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c5">k</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><div><span class="lab"><font color="Green" title="E45">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:56_1_1_1_2_2"/>
<font color="Maroon" title="c1">f</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:56_1_1_1_2_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E3:56_1_1_1_2_2"/><span class="kw">then </span>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#T28" title="TOPREAL1:th.28">TOPREAL1:28</a></span>;<br/><span class="kw">hence </span><a NAME="E4:56_1_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E39">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1_2_3"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1_2_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:56_1_1_1_2_3_1"/>
( ( <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c4">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span> ) or <font color="Maroon" title="c4">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</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">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span> or <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1_2_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2_3_1_1"/><span class="lab"><font color="Green" title="E46">A13</font></span>: 
( <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c4">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><a NAME="E2:56_1_1_1_2_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E3:56_1_1_1_2_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E4:56_1_1_1_2"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="graph_2.html#T13" title="GRAPH_2:th.13">GRAPH_2:13</a></span>;<br/><a NAME="E4:56_1_1_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A14</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E5:56_1_1_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A15</font></span>: 
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <font color="Maroon" title="c2">g</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E6:56_1_1_1_2"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E4:56_1_1_1_2"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="topreal8.html#T31" title="TOPREAL8:th.31">TOPREAL8:31</a></span>;<br/><a NAME="E6:56_1_1_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A16</font></span>: 
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="ref" href="topreal3.html#T26" title="TOPREAL3:th.26">TOPREAL3:26</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1_2_3_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1_2_3_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:56_1_1_1_2_3_1_1_1_1"/>
( <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> or <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1_2_3_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2_3_1_1_1_1_1"/><span class="lab"><font color="Green" title="E50">A17</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><a NAME="E2:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A18</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E3:56_1_1_1_2_3_1_1_1_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A19</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E51">A18</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E5:56_1_1_1_2_3_1_1_1_1_1"/><span class="lab"><font color="Green" title="E53">A20</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56_1_1_1_2"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="realset1.html#T13" title="REALSET1:th.13">REALSET1:13</a></span>;<br/><a NAME="E6:56_1_1_1_2_3_1_1_1_1_1"/><span class="lab"><font color="Green" title="E54">A21</font></span>: 
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56_1"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="txt" href="#E1:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E50">A17</font></span></a>, <a class="ref" href="topreal8.html#T28" title="TOPREAL8:th.28">TOPREAL8:28</a></span>;<br/><a NAME="E7:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal3.html#T26" title="TOPREAL3:th.26">TOPREAL3:26</a></span>;<br/><a NAME="E8:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A22</font></span>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="txt" href="#E6:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E49">A16</font></span></a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></span>;<br/><span class="kw">assume </span><a NAME="E9:56_1_1_1_2_3_1_1_1_1_1"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E11:56_1_1_1_2_3_1_1_1_1_1"/><span class="lab"><font color="Green" title="E56">A23</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font>
 <span class="kw">and </span><br/><a NAME="E12:56_1_1_1_2_3_1_1_1_1_1"/><span class="lab"><font color="Green" title="E57">A24</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><a NAME="E13:56_1_1_1_2_3_1_1_1_1_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E56">A23</font></span></a>, <a class="txt" href="#E12:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E57">A24</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E14:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A25</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E55">A22</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E15:56_1_1_1_2_3_1_1_1_1_1"/>
<font color="Maroon" title="c3">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="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E1:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E50">A17</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E16:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E6:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E54">A21</font></span></a>, <a class="txt" href="#E11:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E56">A23</font></span></a>, <a class="txt" href="#E14:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E58">A25</font></span></a>, <a class="txt" href="#E4:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E52">A19</font></span></a>, <a class="ref" href="goboard2.html#T7" title="GOBOARD2:th.7">GOBOARD2:7</a></span>;<br/><a NAME="E17:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E18:56_1_1_1_2_3_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E19:56_1_1_1_2_3_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E5:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E12:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E57">A24</font></span></a>, <a class="txt" href="#E14:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E58">A25</font></span></a>, <a class="txt" href="#E5:56_1_1_1_2_3_1_1_1_1_1"><span class="lab"><font color="Green" title="E53">A20</font></span></a>, <a class="ref" href="jordan5b.html#T33" title="JORDAN5B:th.33">JORDAN5B:33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="56_1_1_1_2_3_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2_3_1_1_1_1_2"/>
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">l</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:56_1_1_1_2_3_1_1_1_1_2"/><span class="lab"><font color="Green" title="E50">A26</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">l</font> = <font color="Maroon" title="c7">l</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E5:56_1_1_1_2_3_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2_3_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A26</font></span></a></span>;<br/><a NAME="E6:56_1_1_1_2_3_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E7:56_1_1_1_2_3_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A27</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/><a NAME="E8:56_1_1_1_2_3_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E9:56_1_1_1_2_3_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E10:56_1_1_1_2_3_1_1_1_1_2"/><span class="kw">then </span>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <font color="Maroon" title="c2">g</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E6:56_1_1_1_2"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E4:56_1_1_1_2"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="topreal8.html#T31" title="TOPREAL8:th.31">TOPREAL8:31</a></span>;<br/><span class="kw">hence </span><a NAME="E11:56_1_1_1_2_3_1_1_1_1_2"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E5:56_1_1_1_2_3_1_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E3:56_1_1_1_2_3_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A26</font></span></a>, <a class="txt" href="#E7:56_1_1_1_2_3_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A27</font></span></a>, <a class="ref" href="topreal1.html#D9" title="TOPREAL1:def.9">TOPREAL1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="kw">hence </span><a NAME="E8:56_1_1_1_2_3_1_1"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="56_1_1_1_2_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2_3_1_2"/>
<font color="Maroon" title="c4">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</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">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><a NAME="E2:56_1_1_1_2_3_1_2"/><span class="kw">then </span>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#D5" title="TOPREAL1:def.5">TOPREAL1:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:56_1_1_1_2_3_1_2"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="56_1_1_1_2_3_1_3"><span class="kw">suppose </span></a><a NAME="E1:56_1_1_1_2_3_1_3"/>
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font></span><br/><div class="add"><a NAME="E2:56_1_1_1_2_3_1_3"/><span class="kw">then </span>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#D5" title="TOPREAL1:def.5">TOPREAL1:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:56_1_1_1_2_3_1_3"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="kw">hence </span><a NAME="E8:56_1_1_1_2"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="kw">hence </span><a NAME="E5:56_1"/>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c4">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:56"/>
<font color="Maroon" title="c1">f</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c2">g</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#D9" title="TOPREAL1:def.9">TOPREAL1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
