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<div><span class="kw">theorem </span><a NAME="T46"><span class="comment"><font color="firebrick">:: MSAFREE4:46</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">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="struct_0.html#NM8" title="STRUCT_0:NM.8">ManySortedSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">T</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="msafree4.html#V5" title="MSAFREE4:attr.5">-terms</a>   <a href="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</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="b4">A</font> being   <a href="msafree4.html#NM2" title="MSAFREE4:NM.2">image</a> of <font color="Olive" title="b3">T</font><br/>  for <font color="Olive" title="b5">G</font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Olive" title="b3">T</font>  st <font color="Olive" title="b5">G</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Olive" title="b2">X</font> holds <br/> for <font color="Olive" title="b6">f</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive" title="b5">G</font>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">A</font>  ex <font color="Olive" title="b7">h</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b3">T</font>,<font color="Olive" title="b4">A</font> st <br/>( <font color="Olive" title="b7">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b3">T</font>,<font color="Olive" title="b4">A</font> &amp; <font color="Olive" title="b6">f</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b7">h</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <font color="Olive" title="b5">G</font> )</div></div>
