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<div>:: <span class="kw">deftheorem </span>   defines <a href="group_9.html#V9" title="GROUP_9:attr.9">strictly_decreasing</a> <a onclick="hs(this)" href="javascript:()">GROUP_9:def 30 : <br/></a><span> for <font color="Olive" title="b1">O</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G</font> being   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Olive" title="b1">O</font><br/>  for <font color="Olive" title="b3">IT</font> being   <a href="group_9.html#NM4" title="GROUP_9:NM.4">CompositionSeries</a> of <font color="Olive" title="b2">G</font> holds <br/> ( <font color="Olive" title="b3">IT</font> is  <a href="group_9.html#V9" title="GROUP_9:attr.9">strictly_decreasing</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#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b3">IT</font> &amp; <font color="Olive" title="b4">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="b3">IT</font> holds <br/> for <font color="Olive" title="b5">H</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b2">G</font><br/>  for <font color="Olive" title="b6">N</font> being   <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b5">H</font>  st <font color="Olive" title="b5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> &amp; <font color="Olive" title="b6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/> not <font color="Olive" title="b5">H</font> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Olive" title="b6">N</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  );<br/></span></div>
