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<b>let </b><font color="Maroon" title="c1">P</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c3">OAF</font> be    <a href="msalimit.html#M1" title="MSALIMIT:mode.1">OrderedAlgFam</a> of <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">B</font> be    <a href="msalimit.html#M2" title="MSALIMIT:mode.2">Binding</a> of <font color="Maroon" title="c3">OAF</font>;<br/><b>let </b><font color="Maroon" title="c5">i</font>, <font color="Maroon" title="c6">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P</font>;<br/>











<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">j</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c7">f</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:8"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="msalimit.html#K1" title="MSALIMIT:func.1">bind</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font>
 ;<br/>

<a NAME="E3:8"/>
<font color="Maroon" title="c6">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">j</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T24" title="ORDERS_2:th.24">ORDERS_2:24</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">f1</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font></span>)</span>, <font color="Maroon" title="c9">f2</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font></span>)</span><b> such that </b><br/><a NAME="E5:8"/><i><font color="Green" title="E9">A3</font></i>: 
( <font color="Maroon" title="c8">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c5">i</font> &amp; <font color="Maroon" title="c9">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c6">j</font> &amp; <font color="Maroon" title="c4">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c8">f1</font> &amp; <font color="Maroon" title="c8">f1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font> )
 <b>by </b><i><a class="txt" href="msalimit.html#E1:8"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="msalimit.html#D2" target="_self" title="MSALIMIT:def.2">Def2</a></i>;<br/>
<b>thus </b><a NAME="E6:8"/>
<font color="Maroon" title="c7">f</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c6">j</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:8"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="msalimit.html#E2:8"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="msalimit.html#E5:8"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="msalimit.html#D3" target="_self" title="MSALIMIT:def.3">Def3</a></i>;<br/>


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