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<span class="kw">let </span><font color="Maroon" title="c3">IT</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  iff <font color="Maroon" title="c3">IT</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">L</font> )</span><br/>

<a NAME="E1:89_1_1"/>
 ex <font color="Olive" title="b1">x1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <font color="Olive" title="b1">x1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:89"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="algstr_1.html#D24" target="_self" title="ALGSTR_1:def.24">Def24</a></span>;<br/>
<a NAME="E2:89_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c2">x</font> is  <a href="algstr_0.html#V23" title="ALGSTR_0:attr.23">left_invertible</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algstr_0.html#D27" title="ALGSTR_0:def.27">ALGSTR_0:def 27</a></span>;<br/>
<a NAME="E3:89_1_1"/>
<font color="Maroon" title="c2">x</font> is  <a href="algstr_0.html#V17" title="ALGSTR_0:attr.17">right_mult-cancelable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:89"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="algstr_0.html#D37" title="ALGSTR_0:def.37">ALGSTR_0:def 37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:89_1_1"/>
( <font color="Maroon" title="c3">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  iff <font color="Maroon" title="c3">IT</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">L</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:89_1_1"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="algstr_0.html#D35" title="ALGSTR_0:def.35">ALGSTR_0:def 35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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