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<b>let </b><font color="Maroon" title="c1">P</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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#V2" title="STRUCT_0:attr.2">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">NB</font> be  <a href="msalimit.html#V1" title="MSALIMIT:attr.1">normalized</a>  <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="E1:13"/><i><font color="Green" title="E9">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/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1"/>
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">j</font> or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1"><b>suppose </b></a><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">j</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:13_1_1"/>
<span class="p1">(<span class="default"><a href="msalimit.html#K2" title="MSALIMIT:func.2">Normalized</a> <font color="Maroon" title="c4">NB</font></span>)</span> <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="c4">NB</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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="msalimit.html#T3" target="_self" title="MSALIMIT:th.3">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_2"><b>suppose </b></a><a NAME="E1:13_1_2"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j</font>
 ;<br/><div class="add"><a NAME="E2:13_1_2"/>
<span class="p1">(<span class="default"><a href="msalimit.html#K2" title="MSALIMIT:func.2">Normalized</a> <font color="Maroon" title="c4">NB</font></span>)</span> <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>  <a href="funcop_1.html#K12" title="FUNCOP_1:func.12">IFEQ</a> <font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c5">i</font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p2">(<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>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" title="MSALIMIT:func.1">bind</a> <font color="Maroon" title="c4">NB</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p3">(<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>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="msalimit.html#D5" target="_self" title="MSALIMIT:def.5">Def5</a></i>;<br/><a NAME="E3:13_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="msalimit.html#K2" title="MSALIMIT:func.2">Normalized</a> <font color="Maroon" title="c4">NB</font></span>)</span> <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>  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13_1_2"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:13_1_2"/>
<span class="p1">(<span class="default"><a href="msalimit.html#K2" title="MSALIMIT:func.2">Normalized</a> <font color="Maroon" title="c4">NB</font></span>)</span> <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="c4">NB</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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13_1_2"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="msalimit.html#D4" target="_self" title="MSALIMIT:def.4">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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