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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: AMISTD_1:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="measure6.html#NV2" title="MEASURE6:NV.2">with_zero</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">with_non-empty_values</a>   <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">IC-Ins-separated</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> over <font color="Olive" title="b1">N</font> holds <br/> ( <font color="Olive" title="b2">S</font> is  <a href="amistd_1.html#V3" title="AMISTD_1:attr.3">standard</a>  iff  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> (<font color="Olive" title="b3">k</font>,<font color="Olive" title="b2">S</font>) &amp; (  for <font color="Olive" title="b4">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> (<font color="Olive" title="b3">k</font>,<font color="Olive" title="b2">S</font>) holds <br/><font color="Olive" title="b3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">j</font> ) ) )</div></div>
