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<div>:: <span class="kw">deftheorem </span>   defines <a href="bagord_2.html#V3" title="BAGORD_2:attr.3">co-ordered</a> <a onclick="hs(this)" href="javascript:()">BAGORD_2:def 9 : <br/></a><span> for <font color="Olive" title="b1">R</font> being    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">M</font> being    <a href="bagord_2.html#M1" title="BAGORD_2:mode.1">RelExtension</a> of  <a href="monoid_1.html#K17" title="MONOID_1:func.17">finite-MultiSet_over</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">M</font><br/>  for <font color="Olive" title="b4">p</font> being    <a href="bagord_2.html#M2" title="BAGORD_2:mode.2">partition</a> of <font color="Olive" title="b3">b</font> holds <br/> ( <font color="Olive" title="b4">p</font> is  <a href="bagord_2.html#V3" title="BAGORD_2:attr.3">co-ordered</a>  iff  for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">p</font> &amp; <font color="Olive" title="b5">i</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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">p</font> holds <br/> for <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">M</font>  st <font color="Olive" title="b6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Olive" title="b7">b2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b6">b1</font> );<br/></span></div>
