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<span class="kw">let </span><font color="Maroon" title="c1">m</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">  for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/>  for <font color="Olive" title="b2">c</font> being   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Olive" title="b1">G</font>  st 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="Olive" title="b2">c</font> holds <br/>(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Olive" title="b2">c</font> is   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Olive" title="b1">G</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font> be   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</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">c</font> being   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font>  st 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="Olive" title="b1">c</font> holds <br/>(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Olive" title="b1">c</font> is   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font> be   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <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"> ( 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="c4">c</font> implies (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</font> is   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:15"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">and </span><br/><a NAME="E2:15"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:15"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
<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="c4">c</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="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</font> is   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">mnc</font> = (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</font> as    <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="graph_2.html#T41" onmouseover="rs('graph_2/T41')" onmouseout="rh()">GRAPH_2:41</a></span>;<br/>
<a NAME="E5:15"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">mnc</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0: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#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="finseq_6.html#D4" onmouseover="rs('finseq_6/D4')" onmouseout="rh()">FINSEQ_6:def 4</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </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">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</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="c5">mnc</font> holds <br/> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span></span></a><div class="add"><a NAME="E1:15_1"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">mnc</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c4">c</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c6">k</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> &amp; <font color="Maroon" title="c6">k</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="c5">mnc</font> implies  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:15_1"/><span class="lab"><font color="Green" title="E13">A6</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">and </span><br/><a NAME="E3:15_1"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
<font color="Maroon" title="c6">k</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="c5">mnc</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">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span><br/><a NAME="E4:15_1"/>
<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <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> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1"><span class="lab"><font color="Green" title="E13">A6</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E6:15_1"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">and </span><br/><a NAME="E7:15_1"/><span class="lab"><font color="Green" title="E15">A8</font></span>: 
<font color="Maroon" title="c7">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="c5">mnc</font>
 <span class="kw">and </span><br/><a NAME="E8:15_1"/><span class="lab"><font color="Green" title="E16">A9</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="ref" href="finseq_6.html#T127" onmouseover="rs('finseq_6/T127')" onmouseout="rh()">FINSEQ_6:127</a></span>;<br/><a NAME="E9:15_1"/><span class="lab"><font color="Green" title="E17">A10</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="nat_1.html#T12" onmouseover="rs('nat_1/T12')" onmouseout="rh()">NAT_1:12</a></span>;<br/><a NAME="E10:15_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c5">mnc</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E8:15_1"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/><a NAME="E11:15_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">i</font></span>)</span> <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> <font color="Maroon" title="c4">c</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><a NAME="E12:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A11</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">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="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/><a NAME="E13:15_1"/><span class="lab"><font color="Green" title="E19">A12</font></span>: 
<font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="ref" href="finseq_6.html#D4" onmouseover="rs('finseq_6/D4')" onmouseout="rh()">FINSEQ_6:def 4</a></span>;<br/><a NAME="E14:15_1"/>
( <font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">i</font></span>)</span> &amp; <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="txt" href="#E8:15_1"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="ref" href="finseq_6.html#D4" onmouseover="rs('finseq_6/D4')" onmouseout="rh()">FINSEQ_6:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E15:15_1"/>
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">mnc</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:15_1"><span class="lab"><font color="Green" title="E19">A12</font></span></a>, <a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E17">A10</font></span></a>, <a class="txt" href="#E12:15_1"><span class="lab"><font color="Green" title="E18">A11</font></span></a>, <a class="ref" href="graph_1.html#D15" onmouseover="rs('graph_1/D15')" onmouseout="rh()">GRAPH_1:def 15</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:15"/>
(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</font> is   <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>   <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c3">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D15" onmouseover="rs('graph_1/D15')" onmouseout="rh()">GRAPH_1:def 15</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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