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<b>let </b><font color="Maroon" title="c1">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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="c2">M</font>, <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">k</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:73"/><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="idea_1.html#K15" title="IDEA_1:func.15">IDEA_P</a> <font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">m</font>
 <b>and </b><br/><a NAME="E2:73"/><i><font color="Green" title="E58">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4
 ;<br/>

<a NAME="E3:73"/><i><font color="Green" title="E59">A3</font></i>: 
<font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K11" title="IDEA_1:func.11">IDEAoperationA</a> <span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <span class="p2">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:73"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="idea_1.html#D15" target="_self" title="IDEA_1:def.15">Def15</a></i>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">m</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="idea_1.html#D12" target="_self" title="IDEA_1:def.12">Def12</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <span class="p2">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>
;<br/>
<b>hence </b><a NAME="E5:73"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">M</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c2">M</font> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">M</font> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">M</font> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">M</font> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> )
 <b>by </b><i><a class="txt" href="idea_1.html#E2:73"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="idea_1.html#E3:73"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a>, <a class="ref" href="idea_1.html#T27" target="_self" title="IDEA_1:th.27">Th27</a></i>;<br/>


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