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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E37">Def4</font></span>   defines <a href="srings_4.html#V1" title="SRINGS_4:attr.1">cap-closed-yielding</a> <a onclick="hs(this)" href="javascript:()">SRINGS_4:def 5 : <br/></a><span> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">S</font> being    <a href="srings_4.html#M1" title="SRINGS_4:mode.1">SemiringFamily</a> of <font color="Olive" title="b2">X</font> holds <br/> ( <font color="Olive" title="b3">S</font> is  <a href="srings_4.html#V1" title="SRINGS_4:attr.1">cap-closed-yielding</a>  iff  for <font color="Olive" title="b4">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> is  <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a>  );<br/></span></div>
