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<div><span class="kw">theorem </span><a NAME="T3"><span class="comment"><font color="firebrick">:: PRVECT_1:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a>   st  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">GS</font> is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>  &amp;  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">GS</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">GS</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">GS</font> &amp;  <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">comp</a> <font color="Olive" title="b1">GS</font> <a href="finseqop.html#R1" title="FINSEQOP:pred.1">is_an_inverseOp_wrt</a>  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">GS</font> holds <br/><font color="Olive" title="b1">GS</font> is   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a></div></div>
