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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E13">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> &amp; <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f</font> )
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">lmn</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c3">f</font></span>)</span>;<br/>
<a NAME="E3:22"/>
<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">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="msscyc_1.html#E1:22"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
<font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <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> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="msscyc_1.html#E2:22"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E5:22"/><b>then </b>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
not <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c3">f</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>;<br/>


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