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<b>thus </b><a NAME="E1:24_1_1"/>
( <font color="Maroon" title="c1">IT</font> is <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a> implies for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">IT</font> holds <br/> ex <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font> st <font color="Olive" title="b2">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">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">IT</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c1">IT</font> is <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font>;<br/>

<b>assume </b><a NAME="E2:24_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">IT</font>
 ;<br/>

<a NAME="E3:24_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> is <a href="algstr_0.html#V23" title="ALGSTR_0:attr.23">left_invertible</a>
 
<b>by </b><i><a class="txt" href="vectsp_1.html#E1:24_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="algstr_0.html#D39" title="ALGSTR_0:def.39">ALGSTR_0:def 39</a></i>;<br/>
<b>hence </b><a NAME="E4:24_1_1_1"/>
 ex <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font> st <font color="Olive" title="b1">y</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">IT</font>
 <b>by </b><i><a class="ref" href="algstr_0.html#D27" title="ALGSTR_0:def.27">ALGSTR_0:def 27</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:24_1_1"/><i><font color="Green" title="E9">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">IT</font> holds <br/> ex <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font> st <font color="Olive" title="b2">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">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">IT</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D39" title="ALGSTR_0:def.39">ALGSTR_0:def 39</a><br/>

<b>assume </b><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">IT</font>
 ;<br/>

<b>hence </b><a NAME="E4:24_1_1"/>
 ex <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font> st <font color="Olive" title="b1">y</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">IT</font>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E2:24_1_1"><i><font color="Green" title="E9">A2</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D27" title="ALGSTR_0:def.27">ALGSTR_0:def 27</a><br/>


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