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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E7">Def7</font></span>   defines <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> <a onclick="hs(this)" href="javascript:()">INTPRO_1:def 7 : <br/></a><span> for <font color="Olive" title="b1">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a>  iff ( <font color="Olive" title="b1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V1" title="INTPRO_1:attr.1">with_FALSUM</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V2" title="INTPRO_1:attr.2">with_int_implication</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V3" title="INTPRO_1:attr.3">with_int_conjunction</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V4" title="INTPRO_1:attr.4">with_int_disjunction</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V5" title="INTPRO_1:attr.5">with_int_propositional_variables</a>  &amp; <font color="Olive" title="b1">E</font> is  <a href="intpro_1.html#V6" title="INTPRO_1:attr.6">with_modal_operator</a>  ) );<br/></span></div>
