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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: STACKS_1:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="stacks_1.html#NM3" title="STACKS_1:NM.3">StackAlgebra</a><br/>  for <font color="Olive" title="b2">s</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="stacks_1.html#K11" title="STACKS_1:func.11">coset</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K7" title="STACKS_1:func.7">push</a> (<font color="Olive" title="b3">e</font>,<font color="Olive" title="b2">s</font>)</span>)</span> &amp; (  not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Olive" title="b2">s</font> implies <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="stacks_1.html#K11" title="STACKS_1:func.11">coset</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K5" title="STACKS_1:func.5">pop</a> <font color="Olive" title="b2">s</font></span>)</span> ) )</div></div>
