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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font>;<br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">D</font>;<br/>







<b>assume </b><a NAME="E1:18"/>
<font color="Maroon" title="c3">d</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c4">B</font>
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c4">B</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp; <font color="Maroon" title="c3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a>, <a class="ref" href="setwiseo.html#D2" title="SETWISEO:def.2">SETWISEO:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">D</font>;<br/><b>reconsider </b><font color="Maroon" title="c6">b'</font> = <font color="Maroon" title="c5">b</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">D</font> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="prvect_1.html#K2" title="PRVECT_1:func.2">product</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span>,<font color="Maroon" title="c5">b</font> = 
<font color="Maroon" title="c4">B</font> <a href="prvect_1.html#K1" title="PRVECT_1:func.1">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span>,<font color="Maroon" title="c6">b'</font>
<b>by </b><i><a class="ref" href="prvect_1.html#D1" target="_self" title="PRVECT_1:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="prvect_1.html#E2:18"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="finseqop.html#T57" title="FINSEQOP:th.57">FINSEQOP:57</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="prvect_1.html#K2" title="PRVECT_1:func.2">product</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c5">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> = 
<font color="Maroon" title="c4">B</font> <a href="prvect_1.html#K1" title="PRVECT_1:func.1">.:</a> <font color="Maroon" title="c6">b'</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span>
<b>by </b><i><a class="ref" href="prvect_1.html#D1" target="_self" title="PRVECT_1:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="prvect_1.html#E2:18"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="finseqop.html#T57" title="FINSEQOP:th.57">FINSEQOP:57</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:18"/>
<font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <font color="Maroon" title="c3">d</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  <a href="prvect_1.html#K2" title="PRVECT_1:func.2">product</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T11" title="BINOP_1:th.11">BINOP_1:11</a></i>;<br/>


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