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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: STACKS_1:20</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>, <font color="Olive" title="b3">s1</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="b4">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/> ( (  <a href="stacks_1.html#K7" title="STACKS_1:func.7">push</a> (<font color="Olive" title="b4">e</font>,<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> <font color="Olive" title="b3">s1</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> <font color="Olive" title="b3">s1</font> ) &amp; (  not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Olive" title="b2">s</font> &amp;  <a href="stacks_1.html#K5" title="STACKS_1:func.5">pop</a> <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> <font color="Olive" title="b3">s1</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> <font color="Olive" title="b3">s1</font> ) )</div></div>
