<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</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"> 2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">a</font></span><br/>



<span class="p1">(<span class="default"><a href="binom.html#K3" title="BINOM:func.3">Nat-mult-left</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">a</font>) = 
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binom.html#K3" title="BINOM:func.3">Nat-mult-left</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c2">a</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#D3" onmouseover="rs('binom/D3')" onmouseout="rh()">BINOM:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#D3" onmouseover="rs('binom/D3')" onmouseout="rh()">BINOM:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" onmouseover="rs('rlvect_1/D4')" onmouseout="rh()">RLVECT_1:def 4</a></span>
;<br/>
<span class="kw">hence </span><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><a href="binom.html#K3" title="BINOM:func.3">Nat-mult-left</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">a</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#D3" onmouseover="rs('binom/D3')" onmouseout="rh()">BINOM:def 3</a></span>
<br/>.= 
2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c2">a</font>

;<br/> <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>
