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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E44">Def20</font></span>   defines <a href="stacks_1.html#K14" title="STACKS_1:func.14">/==</a> <a onclick="hs(this)" href="javascript:()">STACKS_1:def 20 : <br/></a><span> 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">b<sub>2</sub></font> being   <a href="stacks_1.html#V1" title="STACKS_1:attr.1">strict</a>   <a href="stacks_1.html#L1" title="STACKS_1:struct.1">StackSystem</a>  holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="stacks_1.html#K14" title="STACKS_1:func.14">/==</a>  iff (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font> &amp;  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Olive" title="b1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Olive" title="b1">X</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Olive" title="b1">X</font> <a href="stacks_1.html#K3" title="STACKS_1:func.3">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Olive" title="b1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Olive" title="b1">X</font> <a href="stacks_1.html#K4" title="STACKS_1:func.4">+*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Olive" title="b1">X</font></span>)</span></span>)</span> <a href="filter_1.html#K2" title="FILTER_1:func.2">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Olive" title="b1">X</font></span>)</span> &amp; (  for <font color="Olive" title="b3">f</font> being   <a href="orders_1.html#NM3" title="ORDERS_1:NM.3">Choice_Function</a> of <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Olive" title="b1">X</font></span>)</span></span>)</span> holds   the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Olive" title="b1">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Olive" title="b1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font>) ) ) );<br/></span></div>
