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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="finseqop.html#K6" title="FINSEQOP:func.6">the_inverseOp_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_1.html#K3" title="GROUP_1:func.3">inverse_op</a> <font color="Maroon" title="c1">G</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">o</font> = the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font>;<br/>
<a NAME="E1:41"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
( the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> is  <a href="finseqop.html#V1" title="FINSEQOP:attr.1">having_an_inverseOp</a>  &amp;  <a href="group_1.html#K3" title="GROUP_1:func.3">inverse_op</a> <font color="Maroon" title="c1">G</font> <a href="finseqop.html#R1" title="FINSEQOP:pred.1">is_an_inverseOp_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#T35" target="_self" title="GROUP_1:th.35">Th35</a>, <a class="ref" href="group_1.html#T36" target="_self" title="GROUP_1:th.36">Th36</a></span>;<br/>
<a NAME="E2:41"/>
( the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  &amp; the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#T31" target="_self" title="GROUP_1:th.31">Th31</a>, <a class="ref" href="group_1.html#T34" target="_self" title="GROUP_1:th.34">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:41"/>
 <a href="finseqop.html#K6" title="FINSEQOP:func.6">the_inverseOp_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_1.html#K3" title="GROUP_1:func.3">inverse_op</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="finseqop.html#D3" title="FINSEQOP:def.3">FINSEQOP:def 3</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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