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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E81">ThUnionFam</font></span>: <a NAME="T98"><span class="comment"><font color="firebrick">:: GROUP_23:98</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="group_23.html#V6" title="GROUP_23:attr.6">componentwise_strict</a>   <a href="group_20.html#M1" title="GROUP_20:mode.1">Subgroup-Family</a> of <font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">Fam</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Olive" title="b1">G</font></span>)</span>  st <font color="Olive" title="b4">Fam</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">F</font> holds <br/> for <font color="Olive" title="b5">H</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">I</font>  st <font color="Olive" title="b5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F</font> <a href="group_23.html#K18" title="GROUP_23:func.18">.</a> <font color="Olive" title="b6">i</font> holds <br/> for <font color="Olive" title="b7">J</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b2">I</font>  st <font color="Olive" title="b7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">I</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b8">j</font> where <font color="Olive" title="b8">j</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">I</font> : <font color="Olive" title="b3">F</font> <a href="group_23.html#K18" title="GROUP_23:func.18">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F</font> <a href="group_23.html#K18" title="GROUP_23:func.18">.</a> <font color="Olive" title="b8">j</font> </span> } </span>  holds <br/> <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b8">A</font> where <font color="Olive" title="b8">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">G</font> :  ex <font color="Olive" title="b9">K</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b9">K</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">Fam</font> &amp; <font color="Olive" title="b8">A</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="b9">K</font> &amp; <font color="Olive" title="b9">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">H</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_23.html#K3" title="GROUP_23:func.3">Union</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K14" title="PRALG_1:func.14">Carrier</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="group_23.html#K19" title="GROUP_23:func.19">|</a> <font color="Olive" title="b7">J</font></span>)</span></span>)</span></div></div>
