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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E41">Def9</font></span>   defines <a href="fvaluat1.html#K4" title="FVALUAT1:func.4">Pgenerator</a> <a onclick="hs(this)" href="javascript:()">FVALUAT1:def 9 : <br/></a><span> for <font color="Olive" title="b1">K</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="realset2.html#V1" title="REALSET2:attr.1">Field-like</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">v</font> being    <a href="fvaluat1.html#M1" title="FVALUAT1:mode.1">Valuation</a> of <font color="Olive" title="b1">K</font>  st <font color="Olive" title="b1">K</font> is  <a href="fvaluat1.html#V3" title="FVALUAT1:attr.3">having_valuation</a>  holds <br/> <a href="fvaluat1.html#K4" title="FVALUAT1:func.4">Pgenerator</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="fvaluat1.html#K1" title="FVALUAT1:func.1">least-positive</a> <span class="p3">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">v</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/></span></div>
