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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:3_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="algstr_1.html#V2">add-left-cancelable</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="algstr_1.html#V3">add-right-cancelable</a> )
 ;<br/>

<a NAME="E2:3_1_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( ( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font> implies <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> ) &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>1</sub></font> implies <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> ) )
 
<b>by </b><i><a class="ref" href="algstr_1.html#D6">ALGSTR_1:def 6</a>, <a class="ref" href="algstr_1.html#D7">ALGSTR_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="binom.html#V1" target="_self">add-cancelable</a>
 <b>by </b><i><a class="ref" href="binom.html#D3" target="_self">Def3</a></i>;<br/>


</div>
