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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th4</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: MSINST_1:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">U1</font>, <font color="Olive" title="b4">U2</font>, <font color="Olive" title="b5">U3</font> being   <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">F</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b3">U1</font>,<font color="Olive" title="b4">U2</font><br/>  for <font color="Olive" title="b7">G</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b4">U2</font>,<font color="Olive" title="b5">U3</font><br/>  for <font color="Olive" title="b8">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">U1</font>)  st  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">U1</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">U1</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">U2</font> &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">U2</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b5">U3</font> holds <br/> ex <font color="Olive" title="b9">GF</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b3">U1</font>,<font color="Olive" title="b5">U3</font> st <br/>( <font color="Olive" title="b9">GF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">G</font> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a> <font color="Olive" title="b6">F</font> &amp; <font color="Olive" title="b9">GF</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">G</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">F</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b8">x</font></span>)</span> )</div></div>
