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<b>let </b><font color="Maroon" title="c8">D</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c9">F</font>, <font color="Maroon" title="c10">G</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>



<b>consider </b><font color="Maroon" title="c11">g</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <b> such that </b><br/><a NAME="E2:64"/><i><font color="Green" title="E44">A1</font></i>: 
for <font color="Olive" title="b1">d1</font>, <font color="Olive" title="b2">d2</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">d1</font>,<font color="Olive" title="b2">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">d1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b2">d2</font>
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green" title="E45">A2</font></i>: 
 <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="dtconstr.html#D14" target="_self" title="DTCONSTR:def.14">Def14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c14">c</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/><b>thus </b><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c14">c</font></span>)</span> = 
<font color="Maroon" title="c12">a</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c14">c</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c12">a</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c14">c</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">a</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c14">c</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c14">c</font>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font></span>)</span>,<font color="Maroon" title="c14">c</font>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:64"/><b>then </b><i><font color="Green" title="E46">A3</font></i>: 
<font color="Maroon" title="c11">g</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>
 
<b>by </b><i><a class="ref" href="binop_1.html#D3" title="BINOP_1:def.3">BINOP_1:def 3</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green" title="E47">A4</font></i>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T66" title="FINSEQ_1:th.66">FINSEQ_1:66</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">p</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#T66" title="FINSEQ_1:th.66">FINSEQ_1:66</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">a</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/><b>thus </b><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c13">a</font> = 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c13">a</font>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="dtconstr.html#E6:64"><i><font color="Green" title="E47">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c13">a</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>
;<br/><b>thus </b><font color="Maroon" title="c11">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c13">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  = 
<font color="Maroon" title="c13">a</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="dtconstr.html#E6:64"><i><font color="Green" title="E47">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c13">a</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:64"/><b>then </b>
<font color="Maroon" title="c12">p</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c11">g</font>
 
<b>by </b><i><a class="ref" href="binop_1.html#T11" title="BINOP_1:th.11">BINOP_1:11</a></i>;<br/>
<a NAME="E10:64"/><b>then </b>
( <font color="Maroon" title="c11">g</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">F</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">G</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 ) )
 
<b>by </b><i><a class="ref" href="setwiseo.html#D2" title="SETWISEO:def.2">SETWISEO:def 2</a></i>;<br/>
<b>hence </b> <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">G</font></span>)</span> = 
<font color="Maroon" title="c11">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c10">G</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E3:64"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="dtconstr.html#E5:64"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="finsop_1.html#T6" title="FINSOP_1:th.6">FINSOP_1:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c10">G</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Maroon" title="c9">F</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c10">G</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="dtconstr.html#D14" target="_self" title="DTCONSTR:def.14">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Maroon" title="c9">F</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Maroon" title="c10">G</font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:64"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="dtconstr.html#D14" target="_self" title="DTCONSTR:def.14">Def14</a></i>
;<br/><br/>


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