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<div><div><a NAME="S8"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: BIRKHOFF:sch 8</font></span><br/></a><span class="lab"><font color="Green" title="E8">QuotEpi</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  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> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">F<sub>3</sub></font>() <span class="kw">-&gt; </span>  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] } :<br/><div class="add"><a NAME="E5:10"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:10"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 ex <font color="Olive" title="b1">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() st <font color="Olive" title="b1">H</font> <a href="msualg_3.html#R2" title="MSUALG_3:pred.2">is_epimorphism</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()
 <span class="kw">and </span><br/><a NAME="E2:10"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>2</sub></font>()]
 <span class="kw">and </span><br/><a NAME="E3:10"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>()  st <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="msualg_3.html#R6" title="MSUALG_3:pred.6">are_isomorphic</a>  &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">A</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">B</font>]
 <span class="kw">and </span><br/><a NAME="E4:10"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 for <font color="Olive" title="b1">A</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>()<br/>  for <font color="Olive" title="b2">R</font> being   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">MSCongruence</a> of <font color="Olive" title="b1">A</font>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">A</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[ <a href="msualg_4.html#K13" title="MSUALG_4:func.13">QuotMSAlg</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">R</font>)]
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