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<b>let </b><font color="Maroon" title="c4">G</font>, <font color="Maroon" title="c5">H</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c3">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">D</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:12_1_2"/><i><font color="Green" title="E9">A3</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c3">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">D</font> holds  <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="prvect_1.html#K1" title="PRVECT_1:func.1">.:</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>
 <b>and </b><br/><a NAME="E2:12_1_2"/><i><font color="Green" title="E10">A4</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c3">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">D</font> holds  <font color="Maroon" title="c5">H</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="prvect_1.html#K1" title="PRVECT_1:func.1">.:</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c3">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">D</font>;<br/><a NAME="E1:12_1_2_1"/>
<font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="prvect_1.html#K1" title="PRVECT_1:func.1">.:</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:12_1_2"><i><font color="Green" title="E9">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E2:12_1_2_1"/>
<font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:12_1_2"><i><font color="Green" title="E10">A4</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:12_1_2"/>
<font color="Maroon" title="c4">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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